Numerical Analysis Group  -  Computational Science & Engineering Department  -  GOOGLE

Technical reports produced by Group members

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The following recent technical reports are available:

2010

RAL-TR-2010-004 (PDF)
J. A. Scott and M. Tuma
"The importance of structure in algebraic preconditioners"
RAL-TR-2010-001 (PDF)
J. A. Scott
"Numerical Analysis Group Progress Report: January 2008 - December 2009"

2009

RAL-TR-2009-027 (PDF)
J. D. Hogg, J. K. Reid and J. A. Scott
"Design of a multicore sparse Cholesky factorization using DAGs"
RAL-TR-2009-024 (PDF)
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)
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)
M. Arioli, E. H. Georgoulis and D. Login
"Convergence of inexact adaptive finite element solvers for elliptic problems"
RAL-TR-2009-020 (PDF)
M. Arioli
"An analysis of GMRES worst case convergence"
RAL-TR-2009-017 (PDF)
H. S. Dollar
"Properties of linear systems in PDE-constrained optimization. Part I: Distributed control"
RAL-TR-2009-016 (PDF)
I. S. Duff and B. Ucar
"Combinatorial problems in solving linear systems"
RAL-TR-2009-015 (PDF)
J. K. Reid and J. A. Scott
"Partial factorization of a dense symmetric indefinite matrix"
RAL-TR-2009-014 (PDF)
M. Arioli and D. Ruiz
"Flexible deflation in Krylov methods with Chebyshev-based polynomial filters"
RAL-TR-2009-013 (PDF)
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)
J. A. Scott
"A note on a simple constrained ordering for saddle-point systems"
RAL-TR-2009-006 (PDF)
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)
J. D. Hogg, J. K. Reid and J. A. Scott
"A DAG-based sparse Cholesky solver for multicore architectures"
RAL-TR-2009-003 (PDF)
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)
N. I. M. Gould and D. P. Robinson
"A second derivative SQP method: local convergence"
RAL-TR-2009-001 (PDF)
N. I. M. Gould and D. P. Robinson
"A second derivative SQP method: global convergence"

2008

RAL-TR-2008-031 (PDF)
M. Arioli, D. Kourounis, and D. Loghin
"Discrete fractional Sobolev norms for domain decomposition preconditioning"
RAL-TR-2008-029 (revised) (PDF)
J. Hogg
"A DAG-based parallel Cholesky factorization for multicore systems"
RAL-TR-2008-028 (PDF)
N. I. M. Gould and V. Simoncini
"Spectral analysis of saddle point matrices with indefinite leading blocks"
RAL-TR-2008-027 (PDF) Supersedes RAL-TR-2006-031
J. K. Reid and J. A. Scott,
"Guidelines for the development of HSL software"
RAL-TR-2008-026 (PDF)
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)
J. K. Reid and J. A. Scott
"An efficient out-of-core sparse symmetric indefinite direct solver"
RAL-TR-2008-023 (PDF)
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)
N. I. M. Gould and D. P. Robinson
"A second derivative SQP method with imposed descent"
RAL-TR-2008-018 ( (PDF)
T. Rees, H. S. Dollar and A. J. Wathen
"Optimal solvers for PDE-Constrained Optimization"
RAL-TR-2008-017 (PDF)
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)
J.A. Scott
"Scaling and pivoting in an out-of-core sparse direct solver"
RAL-TR-2008-015 (PDF)
J.V. Ashby and J.K. Reid
"Migrating a scientific application from MPI to coarrays"
RAL-TR-2008-014 (Revised) (PDF)
I.S. Duff and B. Ucar
"On the block triangular form of symmetric matrices"
RAL-TR-2008-013 (PDF)
P.R. Amestoy, I.S. Duff, D. Ruiz, and B. Ucar
"A parallel matrix scaling algorithm"
RAL-TR-2008-012 (PDF)
M. Arioli and D. Loghin
"Discrete interpolation norms with applications"
RAL-TR-2008-010 (PDF)
Z.-Z. Bai, I. S. Duff and J.-F. Yin
"Numerical study on incomplete orthogonal factorization preconditioners"
RAL-TR-2008-009 (PDF)
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)
M. Arioli and S. Gratton
"Least-squares problems, normal equations, and stopping criteria for the conjugate gradient method"
RAL-TR-2008-007 (PDF)
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)
M. Arioli and I. S. Duff
"Using FGMRES to obtain backward stability in mixed precision"
RAL-TR-2008-005 (PDF)
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)
M. Arioli
"Roundoff error analysis of orthogonal factorizations of upper Hessenberg rectangular matrices"
RAL-TR-2008-003 (PDF)
M. Arioli and D. Loghin
"Matrix square-root preconditioners for the Steklov-Poincare operator"
RAL-TR-2008-001 (PDF)
J. A. Scott (Editor)
"Numerical Analysis Group Progress Report: January 2006 - December 2007"


2007

RAL-TR-2007-022 (PDF)
H. S. Dollar and J. A. Scott
"A note on fast approximate minimum degree orderings for symmetric matrices with some dense rows"
RAL-TR-2007-021 (PDF)
J. Boyle, M. D. Mihajlovic and J. A. Scott
"HSL_MI20: an efficient AMG preconditioner"
RAL-TR-2007-020 (PDF)
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)
N. I. M. Gould and Ph. L. Toint
"Nonlinear programming without a penalty function or a filter"
RAL-TR-2007-014 (PDF)
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)
C. Cartis, N. I. M. Gould and Ph. L. Toint
"Adaptive cubic overestimation methods for unconstrained optimization"
RAL-TR-2007-006 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
John Reid and Robert W. Numrich,
"Co-arrays in the next Fortran Standard"


2006

RAL-TR-2006-031 (PostScript, PDF) 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) (PostScript, PDF)
I. S. Duff,
"The design and use of a sparse direct solver for skew symmetric matrices"
RAL-TR-2006-026 (revised) (PostScript, PDF)
J. K. Reid and J. A. Scott,
"HSL_OF01, a virtual memory system in Fortran"
RAL-TR-2006-016 (PostScript, PDF)
C. Cartis and N. I. M. Gould,
"Finding a point in the relative interior of a polyhedron"
RAL-TR-2006-015 (PostScript, PDF)
N. I. M. Gould,
"How good are projection methods for convex feasibility problems?"
RAL-TR-2006-014 (PostScript, PDF)
I. S. Duff,
"Sparse system solution and the HSL Library"
RAL-TR-2006-013 (revised) (PostScript, PDF)
J. K. Reid and J. A. Scott,
"An out-of-core sparse Cholesky solver"
RAL-TR-2006-010 (PostScript, PDF)
M. Arioli and D. Loghin,
"Stopping criteria for mixed finite element problems"
RAL-TR-2006-007 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2004 - December 2005."
RAL-TR-2006-001 (PostScript, PDF)
I.S. Duff and J.A. Scott,
"Towards an automatic ordering for a symmetric sparse direct solver"


2005

RAL-TR-2005-026 (PostScript, PDF)
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 (PostScript, PDF)
J. A. Scott and Y. Hu,
"Experiences of sparse direct symmetric solvers"
RAL-TR-2005-011 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
M. Arioli and G. Manzini,
"MI31: a conjugate gradient algorithm implementation with energy-norm stopping criteria"
RAL-TR-2005-001 (PostScript, PDF)
J. K. Reid and J. A. Scott,
"Reducing the total bandwidth of a sparse unsymmetric matrix"


2004

RAL-TR-2004-040 (PostScript, PDF)
I. S. Duff, S. Riyavong and M. B. Van Gijzen,
"Parallel preconditioners based on partitioning sparse matrices"
RAL-TR-2004-036 (PostScript, PDF)
H. S. Dollar, N. I. M. Gould and A. J. Wathen,
"On implicit-factorization constraint preconditioners"
RAL-TR-2004-033 (Revised) (PostScript, PDF)
I. S. Duff,
"Combining direct and iterative methods for the solution of large systems in different application areas"
RAL-TR-2004-032 (PostScript, PDF)
N. I. M. Gould, D. Orban and Ph. L. Toint,
"Numerical methods for large-scale nonlinear optimization"
RAL-TR-2004-031 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould, D. Orban, A. Sartenaer and Ph. L. Toint,
"Sensitivity of trust-region algorithms to their parameters"
RAL-TR-2004-029 (PostScript, PDF)
M. Arioli, M. Baboulin, and S. Gratton,
"Partial condition number for linear least-squares problems"
RAL-TR-2004-026 (PostScript, PDF)
J. A. Scott
"MA42_ELEMENT - a state-of-the-art frontal solver for finite-element applications"
RAL-TR-2004-020 (PostScript, PDF)
I. S. Duff and S. Pralet,
"Strategies for scaling and pivoting for sparse symmetric indefinite problems"
RAL-TR-2004-018 (PostScript, PDF)
J. A. Scott
"Multilevel hybrid spectral element ordering algorithms"
RAL-TR-2004-017 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2002 - December 2003."
RAL-TR-2004-009 (PostScript, PDF)
N. I. M. Gould, C. Sainvitu and Ph. L. Toint,
"A filter-trust-region method for unconstrained optimization"
RAL-TR-2004-006 (PostScript, PDF)
I. S. Duff and J. A. Scott
"Stabilized bordered block diagonal forms for parallel sparse solvers"


2003

RAL-TR-2003-036 (PostScript, PDF)
Y. Hu and J. A. Scott
"HSL_MC73: A fast multilevel Fiedler and profile reduction code"
RAL-TR-2003-024 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff, L. Giraud, J. Langou, and E. Martin,
"Using spectral low rank preconditioners for large electromagnetic calculations"
RAL-TR-2003-022 (PostScript, PDF)
N. I. M. Gould, D. Orban and Ph. L. Toint,
"An interior-point l1-penalty method for nonlinear optimization"
RAL-TR-2003-020 (PostScript, PDF)
Y. Hu and J. A. Scott
"Ordering techniques for singly bordered block diagonal forms for unsymmetric parallel sparse direct solvers"
RAL-TR-2003-019 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint
"FILTRANE, a fortran 95 filter-trust-region package for solving nonlinear feasibility problems"
FUNDP 03/04 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint
"How mature is nonlinear optimization?"
RAL-TR-2003-013 (PostScript, PDF)
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 (PostScript, PDF)
M. Arioli, D. Loghin, and A. J. Wathen
"Stopping criteria for iterations in finite-element methods"
RAL-TR-2003-004 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
M. Arioli,
"A stopping criterion for the Conjugate Gradient algorithm in a finite element method framework"
RAL-TR-2002-033 (PostScript, PDF)
I. S. Duff and J. A. Scott,
"A parallel direct solver for large sparse highly unsymmetric linear systems"
RAL-TR-2002-032 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould and S. Leyffer,
"An introduction to algorithms for nonlinear optimization"
RAL-TR-2002-030 (PostScript, PDF)
J. K. Reid,
"The new features of Fortran 2000"
RAL-TR-2002-029 (PostScript, PDF)
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 (PostScript, PDF)
P. R. Amestoy, I. S. Duff, and C. Voemel,
"Task scheduling in an asynchronous distributed memory multifrontal solver"
RAL-TR-2002-026 (PostScript, PDF)
M. Arioli and G. Manzini,
"Null space algorithm and spanning trees in solving Darcy's equation"
RAL-TR-2002-024 (PostScript, PDF)
I. S. Duff,
"MA57 - A new code for the solution of sparse symmetric definite and indefinite systems"
RAL-TR-2002-021 (PostScript, PDF)
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 (PostScript, PDF)
B. Carpentieri, I. S. Duff, and L. Giraud,
"A class of spectral two-level preconditioners"
RAL-TR-2002-019 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff and C. Voemel,
"Algorithm xxx: a reference model implementation of the Sparse BLAS in Fortran 95"
RAL-TR-2002-016 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
J. A. Scott,
"Parallel frontal solvers for large sparse linear systems"
RAL-TR-2002-010 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2000 - December 2001."
RAL-TR-2002-009 (PostScript, PDF)
N. I. M. Gould, D. Orban and Ph. L. Toint,
"CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited"
RAL-TR-2002-001 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint,
"Preprocessing for quadratic programming"


2001

RAL-TR-2001-039 (PostScript, PDF)
J. K. Reid and J. A. Scott
"Implementing Hager's exchange methods for matrix profile reduction"
RAL-TR-2001-037 (PostScript, PDF)
M. Arioli and G. Manzini
"A network programming approach in solving Darcy's equations by mixed finite-element methods"
RAL-TR-2001-034 (PostScript, PDF)
D. Ruiz,
"A scaling algorithm to equilibrate both row and column norms in matrices"
RAL-TR-2001-033 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff, M. A. Heroux, and R. Pozo,
"The Sparse BLAS"
RAL-TR-2001-026 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint,
"An iterative working-set method for large-scale non-convex quadratic programming"
RAL-TR-2001-023 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint,
"Numerical methods for large-scale non-convex quadratic programming"
RAL-TR-2001-011 (PostScript, PDF)
J. A. Scott,
"The design of a portable parallel frontal solver for chemical process engineering problems"
RAL-TR-2001-006 (PostScript, PDF)
M. Arioli and G. Manzini,
"A null space algorithm for mixed finite element approximation of Darcy's equation"
RAL-TR-2001-005 (PostScript, PDF)
I. S. Duff and C. Voemel,
"Incremental norm estimation for dense and sparse matrices"
RAL-TR-2001-004 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
Y. F. Hu and J. A. Scott,
"Multilevel algorithms for wavefront reduction"
RAL-TR-2000-030 (PostScript, PDF)
J. A. Scott,
"Two-stage ordering for unsymmetric parallel row-by-row frontal solvers"
RAL-TR-2000-014 (PostScript, PDF)
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 (PostScript, PDF)
K. Meerbergen and J. A. Scott,
"The design of a block rational Lanczos code with partial reorthogonalization and implicit restarting"
RAL-TR-2000-010 (PostScript, PDF)
K. Meerbergen,
"The Lanczos method with semi-inner product"
RAL-TR-2000-009 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 1998 - December 1999."


1999

RAL-TR-1999-075 (PostScript, PDF)
J. A. Scott,
"The design of a parallel frontal solver"
RAL-TR-1999-072 (PostScript, PDF)
I. S. Duff,
"The impact of high performance computing in the solution of linear systems: trends and problems"
RAL-TR-1999-059 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint,
"SQP methods for large-scale nonlinear programming"
RAL-TR-1999-054 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff and Jacko Koster,
"On algorithms for permuting large entries to the diagonal of a sparse matrix"
RAL-TR-1999-037 (PostScript, PDF)
J. K. Reid and J. A. Scott,
"Reversing the row order for the row-by-row frontal method"
RAL-TR-1999-035 (PostScript, PDF)
J. A. Scott,
"Row ordering for frontal solvers in chemical process engineering"
RAL-TR-1999-027 (PostScript, PDF)
I. S. Duff and H. A. van der Vorst,
"Developments and trends in the parallel solution of linear systems"
RAL-TR-1999-025 (PostScript, PDF)
K. Meerbergen,
"The rational Lanczos method for the Hermitian eigenvalue problem"
RAL-TR-1999-016 (PostScript, PDF)
C. Keller, N. I. M. Gould and A. J. Wathen,
"Constraint preconditioning for indefinite linear systems"
RAL-TR-1999-011 (PostScript, PDF)
K. Meerbergen,
"Locking and restarting quadratic eigenvalue solvers"


1998

RAL-TR-1998-076 (PostScript, PDF)
I. S. Duff,
"Matrix methods"
RAL-TR-1998-069 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould,
"Iterative methods for ill-conditioned linear systems from optimization"
RAL-TR-1998-060 (PostScript, PDF)
R. W. Numrich and J. K. Reid,
"Co-Array Fortran for parallel programming"
RAL-TR-1998-057 (PostScript, PDF)
J. D. Pryce and J. K. Reid,
"AD01, a Fortran 90 code for automatic differentitation"
RAL-TR-1998-056 (PostScript, PDF)
J. A. Scott,
"A new row ordering strategy for frontal solvers"
RAL-TR-1998-054 (PostScript, PDF)
I. S. Duff,
"Direct Methods"
RAL-TR-1998-052 (PostScript, PDF)
I. S. Duff and H. A. van der Vorst,
"Preconditioning and Parallel Preconditioning"
RAL-TR-1998-051 (PostScript, PDF)
P. Amestoy, I. Duff, and J.-Y. L'Excellent,
"Multifrontal Parallel Distributed Symmetric and Unsymmetric Solvers"
RAL-TR-98-039 (PostScript, PDF)
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 (PostScript, PDF)
J. A. Scott,
"On ordering elements for a frontal solver"
RAL-TR-98-028 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 1996 - December 1997"
RAL-TR-98-027 (PostScript, PDF)
J. K. Reid,
"Implicit scaling of linear least squares problems"
RAL-TR-98-016 (PostScript, PDF)
J. K. Reid and J. A. Scott,
"Ordering symmetric sparse matrices for small profile and wavefront"
RAL-TR-98-005 (PostScript, PDF)
M. J. Daydé, J. Décamps and N. I. M. Gould,
"Subspace-by-Subspace preconditioners for structured linear systems"
RAL-TR-98-003 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould and J. Nocedal,
"The modified absolute-value factorization norm for trust-region minimization"
ENSEEIHT RT/APO/97/3 (PostScript, PDF)
M. J. Daydé, J. Décamps and N. I. M. Gould,
"Solution of Unassembled Linear Systems Using Block Stretching: Preliminary Experiments"
RAL-TR-97-064 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff and Jacko Koster,
"The design and use of algorithms for permuting large entries to the diagonal"
RAL-TR-97-058 (PostScript, PDF)
"R. B. Lehoucq and J. A. Scott,
"Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations"
RAL-TR-97-055 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint,
"A note on the second-order convergence of optimization algorithms using barrier functions"
FUNDP 97/14 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
T. A. Davis and I. S. Duff,
"A combined unifrontal/multifrontal method for unsymmetric sparse matrices"
RAL-TR-97-041 (PostScript, PDF)
J. A. Scott,
"Exploiting zeros in frontal solvers"
RAL-TR-97-031 (PostScript, PDF)
I. S. Duff and R. G. Grimes and J. G. Lewis,
"The Rutherford-Boeing Sparse Matrix Collection"
RAL-TR-97-028 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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) (PostScript, PDF)
I. S. Duff and J. A. Scott,
"A comparison of frontal software with other Harwell Subroutine Library sparse direct solvers"
RAL-TR-96-102 (PostScript, PDF)
I. S. Duff and J. A. Scott,
"A comparison of frontal software with other sparse direct solvers"
RAL-TR-96-096 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff,
"Sparse numerical linear algebra: direct methods and preconditioning"
RAL-TR-96-042 (PostScript, PDF)
A. R. Conn, N. I. M. Gould and Ph. L. Toint,
"Methods for Nonlinear Constraints in Optimization Calculations"
TOMS-96-22, pp.30-45. (PostScript, PDF)
I. S. Duff and J. A. Scott,
"The design of a new frontal code for solving sparse unsymmetric systems"
RAL-TR-96-023 (PostScript, PDF)
R. B. Lehoucq and J. A. Scott,
"An evaluation of Arnoldi based software for sparse nonsymmetric eigenproblems"
RAL-TR-96-022 (PostScript, PDF)
R. B. Lehoucq and J. A. Scott,
"An evaluation of subspace iteration software for sparse nonsymmetric eigenproblems"
RAL-TR-96-015 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group - Progress report. January 1994 - December 1995"
RAL-TR-96-014 (PostScript, (PDF)
M. J. Daydé and I. S. Duff,
"A Blocked Implementation of Level 3 BLAS for RISC Processors"
RAL-TR-96-013 (PostScript, PDF)
J. Cardenal, I. S. Duff, and J. M. Jimenez,
"A projection method for the solution of rectangular systems"
RAL-TR-96-010 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould,
"Constructing appropriate models for large-scale, linearly-constrained, nonconvex, nonlinear optimization algorithms"
RAL-95-027 (PostScript, PDF)
J. A. Scott,
"Element resequencing for use with a multiple front algorithm"
RAL-TR-95-026 (PostScript, PDF)
N. I. M. Gould and J. A. Scott,
"On approximate-inverse preconditioners"
RAL-93-097 (revised) (PostScript, PDF)
J. A. Scott,
"An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices (revised)"
RAL-95-009 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
A. R. Conn, N. I. M. Gould, A. Sartenaer and Ph. L. Toint,
"On Iterated-Subspace Minimization Methods for Nonlinear Optimization"
RAL-94-062 (PostScript, PDF)
I. S. Duff (Editor),
"Numerical Analysis Group - Progress report. January 1991 - December 1993"
RAL-94-040 (PostScript, PDF)
I. S. Duff and J. A. Scott,
"The use of multiple fronts in Gaussian elimination"
RAL-94-019 (PostScript, PDF)
M. J. Daydé and I. S. Duff,
"Porting industrial codes and developing sparse linear solvers on parallel computers"
ENSEEIHT RT/APO/94/4 (PostScript, PDF) 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 (PostScript, PDF)
I. S. Duff and M. J. Daydé,
"The CERFACS experience"
CERFACS TR/PA/94/03 (PostScript, PDF)
A. R. Conn, N. I. M. Gould and Ph. L. Toint,
"Large-scale nonlinear constrained optimization: a current survey"


1993

RAL-93-097 (PostScript, PDF)
J. A. Scott,
"An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices"
RAL-93-084 (PostScript, PDF)
I.S. Duff,
"The solution of augmented systems"
RAL-93-072 (PostScript, PDF)
I. S. Duff and J. K. Reid,
"MA48, a Fortran code for direct solution of sparse unsymmetric linear systems of equations"
RAL-93-066 (PostScript, PDF) 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 (PostScript, PDF)
I. S. Duff and J. A. Scott,
"MA42 - A new frontal code for solving sparse unsymmetric systems"
RAL-93-036 (PostScript, PDF)
T. A. Davis and I. S. Duff,
"An unsymmetric-pattern multifrontal method for sparse LU factorization"
CERFACS TR/PA/93/27 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF) or the published version in ACM TOMS (PostScript, PDF)
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint,
"CUTE: constrained and unconstrained testing environment"


1992

RAL-92-086 (PostScript, PDF)
I. S. Duff, R. G. Grimes and J. G. Lewis,
"Users' Guide for the Harwell-Boeing Sparse Matrix Collection (Release I)"
RAL-92-069 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
J. K. Reid,
"The advantages of Fortran 90"
FUNDP 92/17 (PostScript, PDF)
A. R. Conn, N. I. M. Gould and Ph. L. Toint,
"A note on exploiting structure when using slack variables"
FUNDP 92/16 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
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 (PostScript, PDF)
I. S. Duff and J. A. Scott,
"Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration"


1970-1990

AERE-R10533 (1982) (PDF)
I. S. Duff and J. K. Reid
"MA27 -- A Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations"
AERE-TP515 (1973) (PDF)
M. D. Hebden
"An algorithm for minimization using exact second derivatives"
AERE-R7125 (1972) (PDF)
R. Fletcher
"Fortran subroutines for minimization by quasi-Newton methods"
AERE-R6799 (1971) (PDF)
R. Fletcher
"A modified Marquardt subroutine for non-linear least squares"
AERE-R6469 (1970) (PDF)
M. J. D. Powell
"A Fortran subroutine for unconstrained minimization, requiring first derivatives of the objective function"


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


2009-1 (PDF)
H. S. Dollar
"On Taylor series approximations for trust-region and regularized subproblems in optimization"
2005-1 revised: (PostScript, PDF), original: (PostScript, PDF)
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"
2004-1 (PostScript, PDF)
J. A. Scott, Y. Hu and N. I. M. Gould
"An evaluation of sparse direct symmetric solvers: an introduction and preliminary findings"
2003-2 (PostScript, PDF)
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 (PostScript, PDF)
N. I. M. Gould
"Some reflections on the current state of active-set and interior-point methods for constrained optimization"
2002-1 (PostScript, PDF)
N. I. M. Gould, D. Orban and Ph. L. Toint
"Results from a numerical evaluation of LANCELOT B"
2000-1 (PostScript, PDF)
N. I. M. Gould and Ph. L. Toint
"A Quadratic Programming Bibliography"

 
Numerical Analysis Group STFC