Technical Reports

2022

RAL-TR-2022-004 (PDF(link opens in a new window))
J. Reid
The new features of Fortran 202x
RAL-TR-2022-002 (PDF(link opens in a new window))
M. O'Flynn, J. Fowkes, N. Gould
Global optimization of crystal field parameter fitting in Mantid

2020

RAL-P-2020-004 (PDF(link opens in a new window))
J. Scott and M. Tuma
A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems
RAL-P-2020-003 (PDF(link opens in a new window))
J. Scott and M. Tuma
A null-space approach for symmetric saddle point systems with a non zero (2,2) block
RAL-P-2020-002 (PDF(link opens in a new window))
T. Rees and M. Wathen
An element-based preconditioner for mixed finite element problems
RAL-P-2020-001 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, P.L. Toint
Strong evaluation comlexity bounds for arbitrary-order optimization of nonconvex nonsmooth composite functions

2019

RAL-TR-2019-005 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, M. Lange
On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces
RAL-TR-2019-004 (PDF(link opens in a new window))
N.I.M. Gould and V. Simoncini
Error estimates for iterative algorithms for minimizing regularized quadratic subproblems
RAL-TR-2019-003 (PDF(link opens in a new window))
T. Davis, I.S. Duff, S. Nakov
Design and implementation of a parallel Markowitz Threshod Algorithm
RAL-TR-2019-001 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees and J.A. Scott
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints
RAL-P-2019-004 (PDF(link opens in a new window))
I. Dauzickaite, A.S. Lawless, J.A. Scott, P.J. van Leeuwen
Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation
RAL-P-2019-002 (PDF(link opens in a new window))
M. Wathen and C. Greif
A scalable approximate inverse block preconditioner for an incompressible magnetohydrodynamics model problem
RAL-P-2019-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Strengths and limitations of stretching for least-squares problems with some dense rows

2018

RAL-P-2018-012 (PDF(link opens in a new window))
I. Duff, J. Hogg, F. Lopez
A new sparse symmetric indefinite solver using a posteriori threshold pivoting
RAL-P-2018-006 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints
RAL-TR-2018-008 (PDF(link opens in a new window))
S. Cayrols, I.S. Duff and F. Lopez
Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model
RAL-P-2018-004 (PDF(link opens in a new window))
I.S. Duff, P.A. Knight, L. le Gorrec, S. Mouysset and D. Ruiz
Uncovering hidden block structure
RAL-P-2018-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Sparse stretching for solving sparse-dense linear least-squares problems

2017

RAL-TR-2017-010 (PDF(link opens in a new window))
I.S. Duff, F. Lopez, S. Nakov
Sparse Direct Solution on Parallel Computers
RAL-P-2017-010 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees, J.A. Scott
A higher order method for solving nonlinear least-squares problems
RAL-P-2017-009 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees, J.A. Scott
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems
RAL-P-2017-008 (PDF(link opens in a new window))
S. Lungten, W.H.A. Schilders and J.A. Scott
Preordering saddle-point systems for sparse LDLT factorization without pivoting
RAL-P-2017-007 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
RAL-TR-2017-006 (PDF(link opens in a new window))
I.S. Duff and F. Lopez
Experiments with sparse Cholesky using a parametrized task graph implementation
RAL-P-2017-006 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
RAL-P-2017-005 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Optimality of orders one to three and beyond : characterization and evaluation complexity in constrained nonconvex optimization
RAL-TR-2017-003 (PDF(link opens in a new window))
I.S. Duff, A.M. Erisman, J.K. Reid
The Hellerman-Rarick algorithm
RAL-P-2017-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows
RAL-P-2017-003 (PDF(link opens in a new window))
F. Furini, E. Traversi, P. Belotti, A. Frangioni, A. Gleixner, N.I.M. Gould, L. Liberti, A. Lodi, R. Misener, H. Mittelmann, N.V. Sahinidis, S. Vigerske and A. Wiegele
QPLIB: A Library of Quadratic Programming Instances
RAL-P-2017-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Solving mixed sparse-dense linear least squares by preconditioned iterative methods

2016

RAL-P-2016-016 (PDF(link opens in a new window))
I.S. Duff, J. Hogg and F. Lopez
Experiments with sparse Cholesky using a sequential task-flow implementation
RAL-P-2016-010 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Universal regularization methods-varying the power, the smoothness and the accuracy
RAL-P-2016-009 (PDF(link opens in a new window))
J. Hogg, J. Hook, J.A. Scott and F. Tisseur
A max-plus approach to incomplete Cholesky factorization preconditioners
RAL-P-2016-008 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Second-order optimality and beyond: characterization and evaluation complexity in nonconvex convexly-constrained optimization
RAL-P-2016-006 (PDF(link opens in a new window))
E. Chow and J.A. Scott
On the use of iterative methods and blocking for solving sparse triangular systems in incomplete factorization preconditioning
RAL-P-2016-005 (PDF(link opens in a new window))
J.A. Scott
On using Cholesky-based factorizations for solving rank-deficient sparse linear least-squares problems
RAL-P-2016-004 (PDF(link opens in a new window))
J.D. Hogg, J.A. Scott and H.S. Thorne
Numerically-aware orderings for sparse symmetric linear systems
RAL-P-2016-003 (PDF(link opens in a new window))
N.I.M. Gould and D.P. Robinson
A dual gradient-projection method for large-scale strictly convex quadratic probems
RAL-P-2016-002 (PDF(link opens in a new window))
D. Packwood, J.R. Kermode, L. Mones, N. Bernstein, J Woolley, N.I.M. Gould, C. Ortner and G. Csanyi
A universal preconditioner for simulating condensed phase materials
RAL-P-2016-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Preconditioning of linear least squares by RIF for implicitly held normal equations

2015

RAL-TR-2015-011 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models
RAL-P-2015-010 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
The state-of-the-art of preconditioners for sparse linear least-squares problems
RAL-TR-2015-010 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
RAL-TR-2015-009 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
The state-of-the-art of preconditioners for sparse linear least-squares problems: the complete results
RAL-P-2015-005 (PDF(link opens in a new window))
P. Dunning, E. Ovtchinnikov, J.A. Scott and A. Kim
Level-set topology optimization with many linear buckling constraints using an efficient robust eigensolver
RAL-P-2015-004 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
A note on performance profiles for benchmarking software
RAL-P-2015-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Solving symmetric indefinite systems using memory efficient incomplete factorization preconditioners

2014

RAL-P-2014-016 (PDF(link opens in a new window))
T. Rees and J.A. Scott
The null-space method and its relationship with matrix factorizations for sparse saddle point systems
RAL-P-2014-014 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
RAL-P-2014-013 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Corrigendum: On the complexity of finding first-order critical pointsb in constrained nonlinear optimization
RAL-P-2014-012 (PDF(link opens in a new window))
N.I.M. Gould, Y. Loh and D.P. Robinson
A filter SQP method : local convergence and numerical results
RAL-P-2014-011 (PDF(link opens in a new window))
F.E. Curtis, N.I.M. Gould, H. Jiang and D.P. Robinson
Adapting augmented Lagrangian methods: algorithms and practical numerical experience
RAL-TR-2014-011 (PDF(link opens in a new window))
J.A. Scott
"Experiments using incomplete Cholesky factorization preconditioners for saddle-point systems arising in interior-point methods"
RAL-TR-2014-006 (PDF(link opens in a new window))
N.I.M. Gould, C. Ortner and D. Packwood
An efficient dimer method with preconditioning and linesearch
RAL-P-2014-007 (PDF(link opens in a new window))
M. Arioli and I.S. Duff
Preconditioning of linear least-squares problems by identifying basic variables
RAL-P-2014-006 (PDF(link opens in a new window))
J.D. Hogg, E. Ovtchinnikov and J.A. Scott
A sparse symmetric indefinite direct solver for GPU architectures
RAL-P-2014-005 (PDF(link opens in a new window))
L.A. Drummond, I.S. Duff, R. Guivarch, D. Ruiz, and M. Zenadi
Partitioning strategies for the Block Cimmino algorithm
RAL-P-2014-004 (PDF(link opens in a new window))
O. Kaya, E. Kayaaslan, B. Uçar, and I.S. Duff
Fill-in reduction in sparse matrix factorizations using hypergraphs
RAL-P-2014-003 (PDF(link opens in a new window))
J.A. Scott and M. Tůma
On signed incomplete Cholesky factorization preconditioners for saddle-point systems
RAL-P-2014-002 (PDF(link opens in a new window))
J.D. Hogg and J.A. Scott
On the efficient scaling of sparse symmetric matrices using an auction algorithm
RAL-P-2014-001 (PDF(link opens in a new window))
F. E. Curtis, N.I.M. Gould, D.P. Robinson and Ph.L. Toint
An interior-point trust-funnel algorithm for nonlinear optimization
RAL-TR-2014-001 (PDF (link opens in a new window))
F. E. Curtis, N.I.M. Gould, D.P. Robinson and Ph.L. Toint
An interior-point trust-funnel algorithm for nonlinear optimization using a squared-violation feasibility measure

2013

RAL-P-2013-010 (PDF (link opens in a new window))
T. Drummond, I.S. Duff, R. Guivarch, D. Ruiz, and M. Zenadi
Partitioning strategies for the block Cimmino algorithm
RAL-P-2013-009 (PDF (link opens in a new window))
C. Cartis, J. M. Fowkes and N.I.M. Gould
Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties
RAL-P-2013-008 (PDF (link opens in a new window))
N.I.M. Gould, Y. Loh and D. D. Robinson
A filter method with unified step computation for nonlinear optimization
RAL-P-2013-007 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
Compressed threshold pivoting for sparse symmetric indefinite systems
RAL-TR-2013-006 (PDF (link opens in a new window))
M. Arioli
Tensor product of random orthogonal matrices
RAL-TR-2013-005 (PDF (link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint
CUTEst : a constrained testing environment with safe threads
RAL-TR-2013-004 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian
RAL-TR-2013-003 (PDF (link opens in a new window))
M. Arioli and D. Orban
Iterative methods for symmetric quasi-definite linear systems. Part 1 : theory
RAL-P-2013-006 (PDF (link opens in a new window))
N.I.M. Gould, D. Orban and T. Rees
Projected Krylov methods for saddle-point systems
RAL-P-2013-005 (PDF) (PDF - link opens in a new window)
J.A. Scott and M. Tuma
On positive semidefinite modification schemes for incomplete Cholesky factorization
RAL-P-2013-004 (PDF (PDF - link opens in a new window))
J.A. Scott and M. Tuma
HSL_M128 : an efficient and robust limited-memory incomplete Cholesky factorization code
RAL-P-2013-003 (PDF (link opens in a new window))
I.S. Duff and K. Kaya
Preconditioners based on strong subgraphs
RAL-P-2013-002 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods
RAL-P-2013-001 (PDF (link opens in a new window))
I.S. Duff, R. Guivarch, D. Ruiz and M Zenadi
The augmented block Cimmino distributed method

2012

RAL-P-2012-009 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
On the effects of scaling on the performance of Ipopt
RAL-P-2012-008 (PDF (link opens in a new window))
P.R. Amestoy, I.S Duff, J-Y L-Excellent and F-H Rouet
Parallel computation of entries of A inverse
RAL-TR-2012-020 (PDF (link opens in a new window))
C. Grief, T. Rees and D.B. Szyld.
Additive Schwarz with variable weights
RAL-P-2012-006 (PDF (link opens in a new window))
M. Arioli, J. Liesen, A. Miedlar, and Z. Strakos.
Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems.
RAL-P-2012-005 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
Achieving bit compatibility in sparse direct solvers
RAL-P-2012-004 (PDF (link opens in a new window))
C. Grief, T. Rees and D.B. Szyld
MPGMRES : a generalized minimum residual method with multiple preconditioners
RAL-TR-2012-015 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the complexity of the steepest-descent with exact linesearches
RAL-TR-2012-009 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
A study of pivoting strategies for tough sparse indefinite systems
RAL-P-2012-003 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
Optimal weighted matchings for rank-deficient sparse matrices
RAL-P-2012-002 (PDF (link opens in a new window))
J.D. Hogg
A fast triangular solve on GPUs
RAL-TR-2012-008 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
How much patience do you have? A worst-case perspective on smooth nonconvex optimization
RAL-TR-2012-007 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
RAL-TR-2012-001 (PDF (link opens in a new window))
J.A. Scott (ed)
Numerical Analysis Group Progress Report January 2010 - December 2011
RAL-P-2012-001 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
New parallel sparse direct solvers for engineering applications

2011

RAL-TR-2011-026 (PDF (link opens in a new window))
M. Arioli, I.S. Duff, J.D. Hogg and H.S. Thorne
Guidelines for the development of MATLAB interfaces for HSL packages (revised for MATLAB 2011a)
RAL-TR-2011-024 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
HSL_MA97 : a bit-compatible multifrontal code for sparse symmetric systems
RAL-TR-2011-023 (PDF (link opens in a new window))
I.S. Duff
European Exascale Software Initiative: numerical libraries, solvers, and algorithms
RAL-TR-2011-022 (PDF (link opens in a new window))
P. A. Browne, C. J. Budd, N.I.M. Gould, H. A. Kim and J.A. Scott
A fast method for binary programming using first order derivatives, with application to topology optimization with buckling constraints
RAL-TR-2011-020 (PDF (link opens in a new window))
J. M. Fowkes, N.I.M. Gould and C. L. Farmer
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions
RAL-TR-2011-019 (PDF (link opens in a new window))
J.A. Scott and Y. Hu
Level-based heuristics and hill climbing for the antibandwidth maximization problem
RAL-TR-2011-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and D.P. Robinson
Trajectory-following methods for large-scale degenerate quadratic programming
RAL-TR-2011-016 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function
RAL-TR-2011-015 (PDF (link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
Guidelines for the development of HSL software, 2011 version
RAL-TR-2011-011 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Optimal Newton-type methods for nonconvex smooth optimization problems
RAL-TR-2011-010 (PDF (link opens in a new window))
M. Arioli and J.A. Scott
Chebyshev acceleration of iterative refinement
RAL-TR-2011-009 (PDF (link opens in a new window))
N.I.M. Gould
How good are extrapolated bi-projection methods for linear feasibility problems?
RAL-TR-2011-008 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the complexity of finding first-order critical points in constrained nonlinear optimization
RAL-TR-2011-007 (PDF (link opens in a new window))
N.I.M. Gould, M. Porcelli and Ph.L. Toint
Updating the regularization parameter in the adaptive cubic regularization algorithm
RAL-TR-2011-006 (PDF (link opens in a new window))
N.I.M. Gould, D.P. Robinson and Ph.L. Toint
Corrigendum: nonlinear programming without a penalty function or a filter
RAL-TR-2011-005 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
RAL-TR-2011-002 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Complexity bounds for second-order optimality in unconstrained optimization
RAL-P-2011-001 (PDF (link opens in a new window))
I.S. Duff and K. Kaya
Preconditioners based on strong components

2010

RAL-TR-2010-031 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
A modern analyse phase for sparse tree-based direct methods
RAL-TR-2010-030 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Evaluation complexity of adaptive cubic regularization methods for convex unconstrianed optimization
RAL-TR-2010-029 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization"
RAL-TR-2010-027 (PDF (link opens in a new window))
P. R. Amestoy, I.S. Duff, Y. Robert, F.-H. Rouet, and B. Ucar
On computing inverse entries of a sparse matrix in an out-of-core environment
RAL-TR-2010-026 (PDF (link opens in a new window))
C. L. Farmer, J. M. Fowkes and N.I.M. Gould
Optimal multilateral well placement
RAL-TR-2010-022 (PDF (link opens in a new window))
F. W. Wubs and J. Thies
A robust two-level incomplete factorization for (Navier-)Stokes saddle point matrices
RAL-TR-2010-019 (PDF (link opens in a new window))
E.E. Ovtchinnkov and J.K. Reid
A preconditioned block conjugate gradient algorithm for computing extreme eigenpairs of symmetric and Hermitian problems
RAL-TR-2010-016 (PDF (link opens in a new window))
H.S. Thorne
Distributed control and constraint preconditioners
RAL-TR-2010-013 (PDF (link opens in a new window))
M. Arioli, I.S. Duff, N.I.M. Gould, J.D. Hogg, and H.S. Thorne
Guidelines for development of Matlab interfaces for HSL packages
RAL-TR-2010-011 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
An indefinite sparse direct solver for large problems on multicore machines
RAL-TR-2010-008 (PDF (PDF - link opens in a new window))
M. Arioli
Generalized Golub-Kahan bidiagonalization and stopping criteria
RAL-TR-2010-007 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
A note on the solve phase of a multicore solver
RAL-TR-2010-004 (PDF (link opens in a new window))
J.A. Scott and M. Tuma
The importance of structure in algebraic preconditioners
RAL-TR-2010-001 (PDF (link opens in a new window))
J.A. Scott
Numerical Analysis Group Progress Report: January 2008 - December 2009
RAL-P-2010-001 (PDF (link opens in a new window))
I.S. Duff, K. Kaya and B. Ucar
Design, implementation, and analysis of maximum transversal algorithms

2009

RAL-TR-2009-027 (PDF (PDF - link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
Design of a multicore sparse Cholesky factorization using DAGs
RAL-TR-2009-024 (PDF (PDF - link opens in a new window))
N.I.M. Gould and D.P. Robinson
A second-derivative trust-region SQP method with a 'trust-region-free' predictor step
RAL-TR-2009-023 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
On the complexity of steepest descent, Newton's method and regularized Newton methods for nonconvex unconstrained optimization
RAL-TR-2009-021 (PDF (PDF - link opens in a new window))
M. Arioli, E. H. Georgoulis and D. Login
Convergence of inexact adaptive ﬁnite element solvers for elliptic problems
RAL-TR-2009-020 (PDF (PDF - link opens in a new window))
M. Arioli
An analysis of GMRES worst case convergence
RAL-TR-2009-018 (PDF (PDF - link opens in a new window))
H.S. Thorne
Properties of linear systems in PDE-constrained optimization. Part II: Neumann boundary control
RAL-TR-2009-017 (PDF (PDF - link opens in a new window))
H.S. Thorne
Properties of linear systems in PDE-constrained optimization. Part I: Distributed control
RAL-TR-2009-016 (PDF (PDF - link opens in a new window))
I.S. Duff and B. Ucar
Combinatorial problems in solving linear systems
RAL-TR-2009-015 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
Partial factorization of a dense symmetric indefinite matrix
RAL-TR-2009-014 (PDF (PDF - link opens in a new window))
M. Arioli and D. Ruiz
Flexible deflation in Krylov methods with Chebyshev-based polynomial filters
RAL-TR-2009-013 (PDF (PDF - link opens in a new window))
I.S. Duff and D. Mijuca
On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics"
RAL-TR-2009-007 (PDF (PDF - link opens in a new window))
J.A. Scott
A note on a simple constrained ordering for saddle-point systems
RAL-TR-2009-006 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity"
RAL-TR-2009-004 (revised as RAL-TR-2009-027) (PDF (PDF - link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
A DAG-based sparse Cholesky solver for multicore architectures
RAL-TR-2009-003 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould and D.P. Robinson
On solving trust-region and other regularised subproblems in optimization
RAL-TR-2009-002 (PDF (PDF - link opens in a new window))
N.I.M. Gould andD.P. Robinson
A second derivative SQP method: local convergence
RAL-TR-2009-001 (PDF (PDF - link opens in a new window))
N.I.M. Gould andD.P. Robinson
A second derivative SQP method: global convergence

2008

RAL-TR-2008-031 (PDF (PDF - link opens in a new window))
M. Arioli, D. Kourounis, and D. Loghin
Discrete fractional Sobolev norms for domain decomposition preconditioning
RAL-TR-2008-029 (revised) (PDF (PDF - link opens in a new window))
J. Hogg
A DAG-based parallel Cholesky factorization for multicore systems
RAL-TR-2008-028 (PDF (PDF - link opens in a new window))
N.I.M. Gould and V. Simoncini
Spectral analysis of saddle point matrices with indefinite leading blocks
RAL-TR-2008-027 (PDF (PDF - link opens in a new window)) Supersedes RAL-TR-2006-031
J.K. Reid and J.A. Scott,
Guidelines for the development of HSL software
RAL-TR-2008-026 (PDF (PDF - link opens in a new window))
S. Bellavia, C. Cartis, N.I.M. Gould, B. Morini and Ph.L. Toint
Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares
RAL-TR-2008-024 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
An efficient out-of-core sparse symmetric indefinite direct solver
RAL-TR-2008-023 (PDF (PDF - link opens in a new window))
J.D. Hogg and J.A. Scott
A fast and robust mixed precision solver for the solution of sparse symmetric linear systems
RAL-TR-2008-019 (PDF (PDF - link opens in a new window))
N.I.M. Gould and D.P. Robinson
A second derivative SQP method with imposed descent
RAL-TR-2008-018 (PDF (PDF - link opens in a new window))
T. Rees, H.S. Dollar and A.J. Wathen
Optimal solvers for PDE-Constrained Optimization
RAL-TR-2008-017 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, M. Stoll and A.J. Wathen
A Bramble-Pasciak-like method with applications in optimization
RAL-TR-2008-016 (PDF (PDF - link opens in a new window))
J.A. Scott
Scaling and pivoting in an out-of-core sparse direct solver
RAL-TR-2008-015 (PDF (PDF - link opens in a new window))
J.V. Ashby and J.K. Reid
Migrating a scientific application from MPI to coarrays
RAL-TR-2008-014 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff and B. Ucar
On the block triangular form of symmetric matrices
RAL-TR-2008-013 (PDF (PDF - link opens in a new window))
P.R. Amestoy, I.S. Duff, D. Ruiz, and B. Ucar
A parallel matrix scaling algorithm
RAL-TR-2008-012 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin
Discrete interpolation norms with applications
RAL-TR-2008-010 (PDF (PDF - link opens in a new window))
Z.-Z. Bai, I.S. Duff and J.-F. Yin
Numerical study on incomplete orthogonal factorization preconditioners
RAL-TR-2008-009 (PDF (PDF - link opens in a new window))
I.S. Duff and D. Mijuca
On the efficient solution of mixed finite element equations in geometrically multiscale thermal stress analysis
RAL-TR-2008-008 (PDF (PDF - link opens in a new window))
M. Arioli and S. Gratton
Least-squares problems, normal equations, and stopping criteria for the conjugate gradient method
RAL-TR-2008-007 (PDF (PDF - link opens in a new window))
J.D. Hogg and J.A. Scott
The Effects of Scalings on the Performance of a Sparse Symmetric Indefinite Solver
RAL-TR-2008-006 (PDF (PDF - link opens in a new window))
M. Arioli and I.S. Duff
Using FGMRES to obtain backward stability in mixed precision
RAL-TR-2008-005 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Trust-region and other regularisations of linear least-squares problems
RAL-TR-2008-004 (PDF (PDF - link opens in a new window))
M. Arioli
Roundoff error analysis of orthogonal factorizations of upper Hessenberg rectangular matrices
RAL-TR-2008-003 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin
Matrix square-root preconditioners for the Steklov-Poincare operator
RAL-TR-2008-001 (PDF (PDF - link opens in a new window))
J.A. Scott (Editor)
Numerical Analysis Group Progress Report: January 2006 - December 2007

2007

RAL-TR-2007-022 (PDF (PDF - link opens in a new window))
H. S. Dollar and J.A. Scott
A note on fast approximate minimum degreeorderings for symmetric matrices with some dense rows
RAL-TR-2007-021 (PDF (PDF - link opens in a new window))
J. Boyle, M. D. Mihajlovic and J.A. Scott
HSL_MI20: an efficient AMG preconditioner
RAL-TR-2007-020 (PDF (PDF - link opens in a new window))
P.R. Amestoy, H. S. Dollar, J.K. Reid and J.A. Scott
An approximate minimum degree algorithm for matrices with dense rows
RAL-TR-2007-016 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
Nonlinear programming without a penalty function or a filter
RAL-TR-2007-014 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems
RAL-TR-2007-007 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Adaptive cubic overestimation methods for unconstrained optimization
RAL-TR-2007-006 (PDF (PDF - link opens in a new window))
P. Amestoy, I.S. Duff, A. Guermouche, and T. Slavova,
Analysis of the out-of-core solution phase of a parallel multifrontal approach
RAL-TR-2007-002 (PDF (PDF - link opens in a new window))
I.S. Duff, S. Gratton, X, Pinel, and X. Vasseur,
Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics
RAL-TR-2007-001 (PDF (PDF - link opens in a new window))
John Reid and Robert W. Numrich,
Co-arrays in the next Fortran Standard

2006

RAL-TR-2006-031 (PDF (PDF - link opens in a new window)) Superseded by RAL-TR-2008-027
J.K. Reid and J.A. Scott,
Guidelines for the development of HSL software
RAL-TR-2006-027 (revised) (PDF (PDF - link opens in a new window))
I.S. Duff,
The design and use of a sparse direct solver for skew symmetric matrices
RAL-TR-2006-026 (revised) (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
HSL_OF01, a virtual memory system in Fortran
RAL-TR-2006-016 (PDF (PDF - link opens in a new window))
C. Cartis and N.I.M. Gould,
Finding a point in the relative interior of a polyhedron
RAL-TR-2006-015 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
How good are projection methods for convex feasibility problems?
RAL-TR-2006-014 (PDF (PDF - link opens in a new window))
I.S. Duff,
Sparse system solution and the HSL Library
RAL-TR-2006-013 (revised) (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
An out-of-core sparse Cholesky solver
RAL-TR-2006-010 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin,
Stopping criteria for mixed finite element problems
RAL-TR-2006-007 (PDF (PDF - link opens in a new window))
M. Arioli, I.S. Duff, S. Gratton, and S. Pralet,
A note on GMRES preconditioned by a perturbed LDL^T decomposition with static pivoting
RAL-TR-2006-006 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group Progress Report. January 2004 - December 2005.
RAL-TR-2006-001 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
Towards an automatic ordering for a symmetric sparse direct solver

2005

RAL-TR-2005-026 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, W.H.A. Schilders and A.J. Wathen,
Using constraint preconditioners with regularized saddle-point problems
RAL-TR-2005-014 (PDF (PDF - link opens in a new window))
J.A. Scott and Y. Hu,
Experiences of sparse direct symmetric solvers
RAL-TR-2005-011 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, W.H.A. Schilders and A.J. Wathen,
On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems
RAL-TR-2005-007 (PDF (PDF - link opens in a new window))
I.S. Duff and S. Pralet,
Towards a stable static pivoting strategy for the sequential and parallel solution of sparse symmetric indefinite systems
RAL-TR-2005-005 (PDF (PDF - link opens in a new window))
N.I.M. Gould, Y. Hu and J.A. Scott,
A numerical evaluation of sparse direct symmetric solvers for the solution of large sparse, symmetric linear systems of equations
RAL-TR-2005-004 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
MI31: a conjugate gradient algorithm implementation with energy-norm stopping criteria
RAL-TR-2005-001 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
Reducing the total bandwidth of a sparse unsymmetric matrix

2004

RAL-TR-2004-040 (PDF (PDF - link opens in a new window))
I.S. Duff, S. Riyavong and M. B. Van Gijzen,
Parallel preconditioners based on partitioning sparse matrices
RAL-TR-2004-036 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould and A.J. Wathen,
On implicit-factorization constraint preconditioners
RAL-TR-2004-033 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff,
Combining direct and iterative methods for the solution of large systems in different application areas
RAL-TR-2004-032 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
Numerical methods for large-scale nonlinear optimization
RAL-TR-2004-031 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz
On the convergence of successive linear-quadratic programming algorithms
RAL-TR-2004-030 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
Sensitivity of trust-region algorithms to their parameters
RAL-TR-2004-029 (PDF (PDF - link opens in a new window))
M. Arioli, M. Baboulin, and S. Gratton,
Partial condition number for linear least-squares problems
RAL-TR-2004-026 (PDF (PDF - link opens in a new window))
J.A. Scott
MA42_ELEMENT - a state-of-the-art frontal solver for finite-element applications
RAL-TR-2004-020 (PDF (PDF - link opens in a new window))
I.S. Duff and S. Pralet,
Strategies for scaling and pivoting for sparse symmetric indefinite problems
RAL-TR-2004-018 (PDF (PDF - link opens in a new window))
J.A. Scott
Multilevel hybrid spectral element ordering algorithms
RAL-TR-2004-017 (PDF (PDF - link opens in a new window))
B. S. Andersen, J.A. Gunnels, F. G. Gustavson, J.K. Reid, and J. Wasniewski,
A fully portable high performance minimal storage hybrid format Cholesky algorithm
RAL-TR-2004-016 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group Progress Report. January 2002 - December 2003.
RAL-TR-2004-009 (PDF (PDF - link opens in a new window))
N.I.M. Gould, C. Sainvitu and Ph.L. Toint,
A filter-trust-region method for unconstrained optimization
RAL-TR-2004-006 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott
Stabilized bordered block diagonal forms for parallel sparse solvers

2003

RAL-TR-2003-036 (PDF (PDF - link opens in a new window))
Y. Hu and J.A. Scott
HSL_MC73: A fast multilevel Fiedler and profile reduction code
RAL-TR-2003-024 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, L. Giraud, and G. Sylvand,
Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations
RAL-TR-2003-023 (PDF (PDF - link opens in a new window))
I.S. Duff, L. Giraud, J. Langou, and E. Martin,
Using spectral low rank preconditioners for large electromagnetic calculations
RAL-TR-2003-022 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
An interior-point l₁-penalty method for nonlinear optimization
RAL-TR-2003-020 (PDF (PDF - link opens in a new window))
Y. Hu and J.A. Scott
Ordering techniques for singly bordered block diagonal forms for unsymmetric parallel sparse direct solvers
RAL-TR-2003-019 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott
A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations
RAL-TR-2003-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
FILTRANE, a fortran 95 filter-trust-region package for solving nonlinear feasibility problems
FUNDP 03/04 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
How mature is nonlinear optimization?
RAL-TR-2003-013 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz
On the convergence of successive linear programming algorithms
RAL-TR-2003-009 (PDF (PDF - link opens in a new window))
M. Arioli, D. Loghin, and A.J. Wathen
Stopping criteria for iterations in finite-element methods
RAL-TR-2003-004 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Leyffer and Ph.L. Toint
A multidimensional Filter algorithm for nonlinear equations and nonlinear least squares
RAL-TR-2003-003 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
Global convergence of a non-monotone trust-region SQP-Filter algorithm for nonlinear programming

2002

RAL-TR-2002-034 (PDF (PDF - link opens in a new window))
M. Arioli,
A stopping criterion for the Conjugate Gradient algorithm in a finite element method framework
RAL-TR-2002-033 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
A parallel direct solver for large sparse highly unsymmetric linear systems
RAL-TR-2002-032 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz,
An active set algorithm for nonlinear programming using linear programming and equality constrained subproblems
RAL-TR-2002-031 (PDF (PDF - link opens in a new window))
N.I.M. Gould and S. Leyffer,
An introduction to algorithms for nonlinear optimization
RAL-TR-2002-030 (PDF (PDF - link opens in a new window))
J.K. Reid,
The new features of Fortran 2000
RAL-TR-2002-029 (PDF (PDF - link opens in a new window))
S.A. Forth, M. Tadjouddine, J.D. Pryce and J.K. Reid,
Jacobian code generated by source transformation and vertex elimination is as efficient as hand coding
RAL-TR-2002-028 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, and C. Voemel,
Task scheduling in an asynchronous distributed memory multifrontal solver
RAL-TR-2002-026 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
Null space algorithm and spanning trees in solving Darcy's equation
RAL-TR-2002-024 (PDF (PDF - link opens in a new window))
I.S. Duff,
MA57 - A new code for the solution of sparse symmetric definite and indefinite systems
RAL-TR-2002-021 (PDF (PDF - link opens in a new window))
M. Arioli and D. Ruiz,
A Chebyshev-based two-stage iterative method as an alternative to the direct solution of linear systems
RAL-TR-2002-020 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, and L. Giraud,
A class of spectral two-level preconditioners
RAL-TR-2002-019 (PDF (PDF - link opens in a new window))
A. T. Papadopoulos, I.S. Duff, and A. T. Wathen,
A class of incomplete orthogonal factorization methods. II: implementation and results
RAL-TR-2002-018 (PDF (PDF - link opens in a new window))
I.S. Duff and C. Voemel,
Algorithm xxx: a reference model implementation of the Sparse BLAS in Fortran 95
RAL-TR-2002-016 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, L. Giraud, and M. Magolu monga Made,
Sparse symmetric preconditioners for dense linear systems in electromagnetism
RAL-TR-2002-014 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
RAL-TR-2002-012 (PDF (PDF - link opens in a new window))
J.A. Scott,
Parallel frontal solvers for large sparse linear systems
RAL-TR-2002-010 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group Progress Report. January 2000 - December 2001.
RAL-TR-2002-009 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited
RAL-TR-2002-001 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
Preprocessing for quadratic programming

2001

RAL-TR-2001-039 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
Implementing Hager's exchange methods for matrix profile reduction
RAL-TR-2001-037 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini
A network programming approach in solving Darcy's equations by mixed finite-element methods
RAL-TR-2001-034 (PDF (PDF - link opens in a new window))
D. Ruiz,
A scaling algorithm to equilibrate both row and column norms in matrices
RAL-TR-2001-033 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
Global convergence of a hybrid trust-region SQP-Filter algorithm for general nonlinear programming
RAL-TR-2001-032 (PDF (PDF - link opens in a new window))
I.S. Duff, M. A. Heroux, and R. Pozo,
The Sparse BLAS
RAL-TR-2001-026 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
An iterative working-set method for large-scale non-convex quadratic programming
RAL-TR-2001-023 (PDF (PDF - link opens in a new window))
M. Arioli, J. Maryska, M. Rozloznik, and M. Tuma,
Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media
RAL-TR-2001-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
Numerical methods for large-scale non-convex quadratic programming
RAL-TR-2001-011 (PDF (PDF - link opens in a new window))
J.A. Scott,
The design of a portable parallel frontal solver for chemical process engineering problems
RAL-TR-2001-006 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
A null space algorithm for mixed finite element approximation of Darcy's equation
RAL-TR-2001-005 (PDF (PDF - link opens in a new window))
I.S. Duff and C. Voemel,
Incremental norm estimation for dense and sparse matrices
RAL-TR-2001-004 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and X. S. Li,
Performance and tuning of two distributed memory sparse solvers
RAL-TR-2001-003 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and X. S. Li,
Analysis and comparison of two general sparse solvers for distributed memory computers

2000

RAL-TR-2000-040 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
Componentwise fast convergence in the solution of full-rank systems of nonlinear equations
RAL-TR-2000-031 (PDF (PDF - link opens in a new window))
Y. F. Hu and J.A. Scott,
Multilevel algorithms for wavefront reduction
RAL-TR-2000-030 (PDF (PDF - link opens in a new window))
J.A. Scott,
Two-stage ordering for unsymmetric parallel row-by-row frontal solvers
RAL-TR-2000-014 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
Superlinear convergence of primal-dual interior point algorithms for nonlinear programming
RAL-TR-2000-011 (PDF (PDF - link opens in a new window))
K. Meerbergen and J.A. Scott,
The design of a block rational Lanczos code with partial reorthogonalization and implicit restarting
RAL-TR-2000-010 (PDF (PDF - link opens in a new window))
K. Meerbergen,
The Lanczos method with semi-inner product
RAL-TR-2000-009 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, and L. Giraud,
Some sparse pattern selection strategies for robust Frobenius norm minimization preconditioners in electromagnetism
RAL-TR-2000-001 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group Progress Report. January 1998 - December 1999.

1999

RAL-TR-1999-075 (PDF (PDF - link opens in a new window))
J.A. Scott,
The design of a parallel frontal solver
RAL-TR-1999-072 (PDF (PDF - link opens in a new window))
I.S. Duff,
The impact of high performance computing in the solution of linear systems: trends and problems
RAL-TR-1999-059 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and J.Koster,
A fully asynchronous multifrontal solver using distributed dynamic scheduling
RAL-TR-1999-055 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
SQP methods for large-scale nonlinear programming
RAL-TR-1999-054 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, D. Orban and Ph.L. Toint,
A primal-dual trust-region algorithm for minimizing a non-convex function subject to general inequality and linear equality constraints
RAL-TR-1999-045 (PDF (PDF - link opens in a new window))
Z.-Z. Bai, I.S. Duff, and A.J. Wathen,
A class of incomplete orthogonal factorization methods I: methods and theories
RAL-TR-1999-041 (PDF (PDF - link opens in a new window))
R. Fletcher, N.I.M. Gould, S. Leyffer and Ph.L. Toint,
Global convergence of trust-region SQP-filter algorithms for general nonlinear programming
RAL-TR-1999-039 (PDF (PDF - link opens in a new window))
F. Magoules, K. Meerbergen and J.-P. Coyette,
"Application of a domain decomposition method with Lagrange multipliers to acoustic problems arising from the automotive industry"
RAL-TR-1999-030 (PDF (PDF - link opens in a new window))
I.S. Duff and Jacko Koster,
On algorithms for permuting large entries to the diagonal of a sparse matrix
RAL-TR-1999-037 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
Reversing the row order for the row-by-row frontal method
RAL-TR-1999-035 (PDF (PDF - link opens in a new window))
J.A. Scott,
Row ordering for frontal solvers in chemical process engineering
RAL-TR-1999-027 (PDF (PDF - link opens in a new window))
I.S. Duff and H. A. van der Vorst,
Developments and trends in the parallel solution of linear systems
RAL-TR-1999-025 (PDF (PDF - link opens in a new window))
K. Meerbergen,
The rational Lanczos method for the Hermitian eigenvalue problem
RAL-TR-1999-016 (PDF (PDF - link opens in a new window))
C. Keller, N.I.M. Gould and A.J. Wathen,
Constraint preconditioning for indefinite linear systems
RAL-TR-1999-011 (PDF (PDF - link opens in a new window))
K. Meerbergen,
Locking and restarting quadratic eigenvalue solvers

1998

RAL-TR-1998-076 (PDF (PDF - link opens in a new window))
I.S. Duff,
Matrix methods
RAL-TR-1998-069 (PDF (PDF - link opens in a new window))
N.I.M. Gould, M. E. Hribar and J. Nocedal,
On the solution of equality constrained quadratic programming problems arising in optimization
RAL-TR-1998-064 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
Iterative methods for ill-conditioned linear systems from optimization
RAL-TR-1998-060 (PDF (PDF - link opens in a new window))
R. W. Numrich and J.K. Reid,
Co-Array Fortran for parallel programming
RAL-TR-1998-057 (PDF (PDF - link opens in a new window))
J.D. Pryce and J.K. Reid,
AD01, a Fortran 90 code for automatic differentitation
RAL-TR-1998-056 (PDF (PDF - link opens in a new window))
J.A. Scott,
A new row ordering strategy for frontal solvers
RAL-TR-1998-054 (PDF (PDF - link opens in a new window))
I.S. Duff,
Direct Methods
RAL-TR-1998-052 (PDF (PDF - link opens in a new window))
I.S. Duff and H. A. van der Vorst,
Preconditioning and Parallel Preconditioning
RAL-TR-1998-051 (PDF (PDF - link opens in a new window))
P. Amestoy, I. Duff, and J.-Y. L'Excellent,
Multifrontal Parallel Distributed Symmetric and Unsymmetric Solvers
RAL-TR-98-039 (PDF (PDF - link opens in a new window))
P. Amestoy, I. Duff, J.-Y. L'Excellent, and P. Plechac,
PARASOL An Integrated Programming Environment for Parallel Sparse Matrix Solvers
RAL-TR-98-031 (PDF (PDF - link opens in a new window))
J.A. Scott,
On ordering elements for a frontal solver
RAL-TR-98-028 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group Progress Report. January 1996 - December 1997
RAL-TR-98-027 (PDF (PDF - link opens in a new window))
J.K. Reid,
Implicit scaling of linear least squares problems
RAL-TR-98-016 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
Ordering symmetric sparse matrices for small profile and wavefront
RAL-TR-98-005 (PDF (PDF - link opens in a new window))
M.J. Daydé, J. Décamps and N.I.M. Gould,
Subspace-by-Subspace preconditioners for structured linear systems
RAL-TR-98-003 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
A linesearch algorithm with memory for unconstrained optimization

1997

RAL-TR-97-071 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J. Nocedal,
The modified absolute-value factorization norm for trust-region minimization
ENSEEIHT RT/APO/97/3 (PDF (PDF - link opens in a new window))
M.J. Daydé, J. Décamps and N.I.M. Gould,
Solution of Unassembled Linear Systems Using Block Stretching: Preliminary Experiments
RAL-TR-97-064 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
Exploiting Negative Curvature Directions in Linesearch Methods for Unconstrained Optimization
RAL-TR-97-059 (PDF (PDF - link opens in a new window))
I.S. Duff and Jacko Koster,
The design and use of algorithms for permuting large entries to the diagonal
RAL-TR-97-058 (PDF (PDF - link opens in a new window))
"R. B. Lehoucq and J.A. Scott,
Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations
RAL-TR-97-055 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
A note on the second-order convergence of optimization algorithms using barrier functions
FUNDP 97/14 (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould, M. A. Saunders and Ph.L. Toint,
A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization: the complete results
RAL-TR-97-054 (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould, M. A. Saunders and Ph.L. Toint,
A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization
RAL-TR-97-046 (PDF (PDF - link opens in a new window))
T. A. Davis and I.S. Duff,
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
RAL-TR-97-041 (PDF (PDF - link opens in a new window))
J.A. Scott,
Exploiting zeros in frontal solvers
RAL-TR-97-031 (PDF (PDF - link opens in a new window))
I.S. Duff and R. G. Grimes and J. G. Lewis,
The Rutherford-Boeing Sparse Matrix Collection
RAL-TR-97-028 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
Solving the trust-region subproblem using the Lanczos method
RAL-TR-97-012 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
MA62 - A frontal code for sparse positive-definite symmetric systems from finite-element applications
RAL-TR-97-001 (PDF (PDF - link opens in a new window))
K. A. Cliffe, I.S. Duff and J.A. Scott,
Performance issues for frontal schemes on a cache-based high performance computer

1996

CERFACS TR/PA/96/47 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
Use of Computational Kernels in full and Sparse Linear Solvers, Efficient Code Design on High-Performance RISC Processors
RAL-TR-96-102 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
A comparison of frontal software with other Harwell Subroutine Library sparse direct solvers
RAL-TR-96-102 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
A comparison of frontal software with other sparse direct solvers
RAL-TR-96-096 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints
RAL-TR-96-047 (PDF (PDF - link opens in a new window))
I.S. Duff,
Sparse numerical linear algebra: direct methods and preconditioning
RAL-TR-96-042 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Methods for Nonlinear Constraints in Optimization Calculations
TOMS-96-22, pp.30-45. (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
The design of a new frontal code for solving sparse unsymmetric systems
RAL-TR-96-023 (PDF (PDF - link opens in a new window))
R. B. Lehoucq and J.A. Scott,
An evaluation of Arnoldi based software for sparse nonsymmetric eigenproblems
RAL-TR-96-022 (PDF (PDF - link opens in a new window))
R. B. Lehoucq and J.A. Scott,
An evaluation of subspace iteration software for sparse nonsymmetric eigenproblems
RAL-TR-96-015 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group - Progress report. January 1994 - December 1995
RAL-TR-96-014 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
A Blocked Implementation of Level 3 BLAS for RISC Processors
RAL-TR-96-013 (PDF (PDF - link opens in a new window))
J. Cardenal, I.S. Duff, and J. M. Jimenez,
A projection method for the solution of rectangular systems
RAL-TR-96-010 (PDF (PDF - link opens in a new window))
A. C. Damhaug and J.K. Reid,
MA46, a FORTRAN code for direct solution of sparse unsymmetric linear systems of equations from finite-element applications

1995

RAL-TR-95-049 (PDF (PDF - link opens in a new window))
I.S. Duff, M. Marrone, G. Radicati, and C. Vittoli,
Level 3 Basic Linear Algebra Subprograms for sparse matrices: a user level interface
RAL-TR-95-040 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems
RAL-TR-95-039 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
The design of MA48, a code for the direct solution of sparse unsymmetric linear systems of equations
RAL-TR-95-037 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
Constructing appropriate models for large-scale, linearly-constrained, nonconvex, nonlinear optimization algorithms
RAL-95-027 (PDF (PDF - link opens in a new window))
J.A. Scott,
Element resequencing for use with a multiple front algorithm
RAL-TR-95-026 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott,
On approximate-inverse preconditioners
RAL-93-097 (revised) (PDF (PDF - link opens in a new window))
J.A. Scott,
An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices (revised)
RAL-95-009 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints
RAL-95-001 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
MA47, a Fortran code for direct solution of sparse symmetric linear systems of equations

1994

RAL-94-069 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
On Iterated-Subspace Minimization Methods for Nonlinear Optimization
RAL-94-062 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
Numerical Analysis Group - Progress report. January 1991 - December 1993
RAL-94-040 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
The use of multiple fronts in Gaussian elimination
RAL-94-019 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
Porting industrial codes and developing sparse linear solvers on parallel computers
ENSEEIHT RT/APO/94/4 (PDF (PDF - link opens in a new window)) or RAL-95-010
M.J.Daydé, J.-Y. L'Excellent and N.I.M. Gould,
On the Use of Element-by-Element Preconditioners to Solve Large Scale Partially Separable Optimization Problems
CERFACS TR/PA/94/10 (PDF (PDF - link opens in a new window))
I.S. Duff and M.J.Daydé,
The CERFACS experience
CERFACS TR/PA/94/03 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Large-scale nonlinear constrained optimization: a current survey

1993

RAL-93-097 (PDF (PDF - link opens in a new window))
J.A. Scott,
An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices
RAL-93-084 (PDF (PDF - link opens in a new window))
I.S. Duff,
The solution of augmented systems
RAL-93-072 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
MA48, a Fortran code for direct solution of sparse unsymmetric linear systems of equations
RAL-93-066 (PDF (PDF - link opens in a new window)) or CERFACS TR/PA/93/34
M. Arioli, T. F. Chan, I.S. Duff, N.I.M. Gould and J.K. Reid,
Computing a search direction for large-scale linearly-constrained nonlinear optimization calculations
RAL-93-064 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
MA42 - A new frontal code for solving sparse unsymmetric systems
RAL-93-036 (PDF (PDF - link opens in a new window))
T. A. Davis and I.S. Duff,
An unsymmetric-pattern multifrontal method for sparse LU factorization
CERFACS TR/PA/93/27 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
Local Convergence Properties of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints
CERFACS TR/PA/93/26 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
Global Convergence of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints
CERFACS TR/PA/93/17 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization
CERFACS TR/PA/93/16 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Improving the decomposition of partially separable functions in the context of large-scale optimization: A first approach
CERFACS TR/PA/93/10 (PDF (PDF - link opens in a new window)) or the published version in ACM TOMS (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould and Ph.L. Toint,
CUTE: constrained and unconstrained testing environment

1992

RAL-92-086 (PDF (PDF - link opens in a new window))
I.S. Duff, R. G. Grimes and J. G. Lewis,
Users' Guide for the Harwell-Boeing Sparse Matrix Collection (Release I)
RAL-92-069 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Convergence properties of minimization algorithms for convex constraints using a structured trust region
RAL-92-068 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds
RAL-92-067 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds
RAL-92-017 (PDF (PDF - link opens in a new window))
J.K. Reid,
The advantages of Fortran 90
FUNDP 92/17 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
A note on exploiting structure when using slack variables
FUNDP 92/16 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization
FUNDP 92/15 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Intensive numerical tests with LANCELOT (Release A): the complete results
CERFACS TR/PA/92/89 (PDF (PDF - link opens in a new window))
P. R. Amestoy, M.J.Daydé, I.S. Duff and P. Morere,
Linear algebra calculations on a virtual shared memory computer
CERFACS TR/PA/92/74 (PDF (PDF - link opens in a new window))
M.J.Daydé, I.S. Duff, and A. Petitet,
A parallel block implementation of Level 3 BLAS for MIMD vector processors

1991

RAL-91-056 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration

1970 - 1990

AERE_TP529 (1973) (PDF(link opens in a new window))
R. Fletcher and M.D. Hebden
Setting up a Numerical Advisory Service
AERE-R10533 (1982) (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid
MA27 -- A Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations
AERE-R8629 (1976) (PDF (PDF - link opens in a new window))
J.K. Reid
Fortran subroutines for handling sparse linear programming bases
AERE-TP515 (1973) (PDF (PDF - link opens in a new window))
M. D. Hebden
An algorithm for minimization using exact second derivatives
AERE-R7125 (1972) (PDF (PDF - link opens in a new window))
R. Fletcher
Fortran subroutines for minimization by quasi-Newton methods
AERE-R6799 (1971) (PDF (PDF - link opens in a new window))
R. Fletcher
A modified Marquardt subroutine for non-linear least squares
AERE-R6469 (1970) (PDF (PDF - link opens in a new window))
M.J.D. Powell
A Fortran subroutine for unconstrained minimization, requiring first derivatives of the objective function
AERE-R5947 (1968) (PDF (PDF - link opens in a new window))
M.J.D. Powell
A Fortran subroutine for solving systems of non-linear algebraic equations
AERE-TP322 (1968) (PDF (PDF - link opens in a new window))
M.J.D. Powell and J.K. Reid
On applying Householder transformations to linear least squares problems

The group has also issued the following Numerical Analysis Group Internal Reports:

2023-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Linear least-squares over the unit simplex
2023-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
A projection method for bound-constrained linear least-squares
2013-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Computing useful sparse Hessian approximations satisfying componentwise secant equations I: using a known sparsity pattern
2011-1 (PDF (PDF - 433kB - link opens in a new window))
J.D. Hogg.
C interfaces to HSL routines
2009-2 (PDF (PDF - link opens in a new window))
N. I. M. Gould, M. Kocvara, D. P. Robinson and Ph. L. Toint
Enriched recursive multi-level optimization
2009-1 (PDF (PDF - link opens in a new window))
H.S. Dollar
On Taylor series approximations for trust-region and regularized subproblems in optimization
2007-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Equivalent saddle-point problems
2006-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
A brief note on the Symmetric Rank-1 secant formula
2005-1 revised: (PDF (PDF - link opens in a new window)), original: (PDF (PDF - link opens in a new window))
N.I.M. Gould, Y. Hu and J.A. Scott.
Complete results from a numerical evaluation of sparse direct solvers for the solution of large, sparse, symmetric linear systems of equations
2004-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Parametric quadratic programming, revisited
2004-1 (PDF (PDF - link opens in a new window))
J.A. Scott, Y. Hu and N.I.M. Gould
An evaluation of sparse direct symmetric solvers: an introduction and preliminary findings
2003-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott
Complete results from a numerical evaluation of HSL packages for the direct-solution of large sparse, symmetric linear systems of equations
2003-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Some reflections on the current state of active-set and interior-point methods for constrained optimization
2002-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint
Results from a numerical evaluation of LANCELOT B
2000-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
A Quadratic Programming Bibliography