# Jennifer Scott

## STFC IM Fellow

## Numerical Linear Algebra

- Email: jennifer.scott@stfc.ac.uk
- Site: Rutherford Appleton Laboratory

**Brief career summary**

After completing her DPhil thesis "A unified analysis of discretisation methods" at Oxford in 1984, Jennifer was awarded a Junior Research Fellowship at St. John's College, Oxford. After eighteen months, she left Oxford to take up a position in the Theoretical Physics Department of the National Radiological Protection Board in south Oxfordshire.

In 1987, Jennifer joined the Numerical Analysis Group at the Harwell Laboratory. The Group moved to the Atlas Centre at the Rutherford Appleton Laboratory in 1990. In 2007, she became the Group Leader, a role she continued until 2018 (with the Group changing its name to the Computational Mathematics Group in 2017). In 2011, Jennifer became an STFC Individual Merit Research Fellow. Much of her work at STFC and that of the Group has been funded by EPSRC research grants. She is the author of many software packages that are available within the HSL Mathematical Software Library.

In 2016, Jennifer was appointed Professor of Mathematics at the University of Reading. She now works part time (2 days a week) for STFC as a Principal Researcher and Fellow in Computational Mathematics and spends the rest of her time at the University of Reading. She was Director at Reading of the EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth from 2016 to 2022 and is now the Director at Reading of the EPSRC Centre for Doctoral Training in Mathematics for our Future Climate (2024-- ). This is a joint centre with Imperial College London and the University of Southampton MFC CDT.

Jennifer has co-authored with her collaborator Miroslav Tuma from Charles University in Prague a research monograph * Algorithms for Sparse Linear Systems, *ISBN: 978-3-031-25819-0 (2023). This is available as open access (funded by the University of Reading) and can be downloaded here.

Jennifer is an elected SIAM Fellow. She was the President of SIAM UKIE (2021--23) and the Vice President (2015--17). She is a Fellow of the Institute of Mathematics and its Applications (IMA) and was an elected member of the IMA Council (2013--16). She is an elected member of the IFIP Working Group 2.5 on Numerical Software, she served on the Women in Mathematics Committee of the London Mathematical Society (2006--14) and on the SIAM Program Committee (2013--16). She is an Associate Editor of ACM Transactions on Mathematical Software and formerly an Associate Editor of the SIAM Journal of Scientific Computing (2016--2022).

**Research interests include:**

- Numerical linear algebra (including direct and iterative methods and preconditioners).
- Algorithm design/implementation, especially for sparse linear systems, sparse least squares.
- Large-scale scientific computation.
- The Mathematics of Planet Earth and Mathematics for our Future Climate.

My key scientific contributions, which have involved studying the underlying mathematics, new analysis and theoretical developments, leading to novel algorithms and mathematical software, include:

- Sparse matrix ordering algorithms (bandwidth and profile minimisation and algorithms designed for challenging symmetric indefinite matrices to limit the need for numerical pivoting while maintaining sparsity and stability);
- Algorithms to improve the efficiency and applicability of direct solvers for sparse linear systems (including novel out-of-core techniques, the introduction of multiple front algorithms for coarse-grained parallelism, the use of single precision within a sparse double precision solver, and sparse matrix scaling algorithms);
- Robust limited memory incomplete factorization preconditioners for sparse linear systems and large-scale sparse (and mixed sparse-dense) least squares problems.

This work has led to the publication of an open access research monograph *Algorithms for Sparse Linear Systems, *ISBN: 978-3-031-25819-0 (2023) [pdf], research papers and software in the HSL and SPRAL Mathematical Software Libraries.

**About the monograph Algorithms for Sparse Linear Systems**

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines.

This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

**Book**

[pdf]*Algorithms for Sparse Linear Systems*

Jennifer Scott and Miroslav Tuma. Springer Birkhauser, Necas Center Series, April 2023. DOI:10.1007/978-3-031-25820-6

**Journal publications**

2024

- Avoiding breakdown in incomplete factorizations in low precision arithmetic [pdf]

Jennifer Scott and Miroslav Tuma. ACM Trans. Math. Softw., 24 pages, published online March 2024. DOI: 10.1145/3651155.

2023

- Approximating sparse Hessian matrices using large-scale linear least squares [pdf]

Jaroslav Fawkes, Nicholas Gould, and Jennifer Scott. Numerical Algorithms, published online November 2023. DOI: 10.1007/s11075-023-01681-z.

2022

- Solving large linear least squares with linear equality constraints [pdf]

Jennifer Scott and Miroslav Tuma. BIT Numerical Mathematics, 2022. DOI: 10.1007/s10543-022-00930-2 - A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems [pdf]

Jennifer Scott and Miroslav Tuma. ACM Trans. Math. Softw., 48, Number 1, Article 5, 24 pages, 2022. DOI: 10.1145/3494527. - A robust algebraic domain decomposition preconditioner for sparse normal equations [pdf]

Hussam Al Daas, Pierre Jolivet, Jennifer Scott. SIAM J. Scientific Computing, 2022, 44(3), A1047--1068. DOI: 10.1137/21M1434891. - A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2,2) block [pdf]

Jennifer Scott and Miroslav Tuma. Numerical Algorithms, 2022, 90, 1639--1667. DOI: 10.1007/s11075-021-01245-z.

2021

- Two-level Nystrom-Schur preconditioner for sparse symmetric positive definite matrices [[pdf]

Hussam Al Daas, Tyrone Rees, Jennifer Scott. SIAM J. Scientific Computing, 2021, 43(6), A3837--A3861. DOI: 10.1137/21M139548X - Randomised preconditioning for the forcing formulation of weak constraint 4D-Var [pdf]

I. Dauzickaite, A.S. Lawless, J.A. Scott and P.J. van Leeuwen. Quarterly Journal of the Royal Meteorological Society, 2021, 147:3719–3734. DOI: 10.1002/qj.4151. - On time-parallel preconditioning for the state formulation of incremental weak constraint 4D-Var [pdf]

I. Dauzickaite, A.S. Lawless, J.A. Scott and P.J. van Leeuwen. Quarterly Journal of the Meteorological Society, 2021, 147:3521–3529. DOI: 10.1002/qj.4140. - Strengths and limitations of stretching for least-squares problems with some dense rows [pdf]

Jennifer Scott and Miroslav Tuma. ACM Trans. Math. Softw., 47, Number 1, Article 1, 25 pages, 2021. DOI: 10.1145/3412559.

2020

- Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation [pdf]

I. Dauzickaite, A.S. Lawless, J.A. Scott and P.J. van Leeuwen. Numer. Lin. Alg. Applics., 27, Number 5, e2313, 24 pages, 2020, DOI: 10.1002/nla.2313

2019

- Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems [pdf]

N.I.M. Gould, T. Rees and J.A. Scott. Computational Optimization and Applications. 73, Number 1, pp 1--35, 2019. DOI: 10.1007/s10589-019-00064-2. - Sparse stretching for solving sparse-dense linear least-squares problems [pdf]

Jennifer Scott and Miroslav Tuma. SIAM J. Sci. Computing. 41, Number 3, pp A1604--A1625, 2019. DOI: 10.1137/18M1181353

2018

- A max-plus approach to incomplete Cholesky factorization preconditioners [pdf]

J. Hook, J. Scott, F. Tisseur and J. Hogg. SIAM J. Sci. Computing. 40, Number 4, pp A1987--A2004, 2018. - Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning [pdf]

E. Chow, H. Antz, J. Scott and J. Dongarra. Journal of Parallel and Distributed Computing, 119, pp 219--230, 2018. - Preordering saddle-point systems for sparse LDLT factorization without pivoting [pdf]

S. Lungten, W. H. A. Schilders and J. A. Scott. Numer. Lin. Alg. Applics., e2173, 2018. DOI: 10.1002/nla.2173. - A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows [pdf]

Jennifer Scott and Miroslav Tuma. Numerical Algorithms. 79, pp 1147--1168, 2018. DOI: 10.1007/s11075-018-0478-2. - A comparative study of null-space factorizations for sparse symmetric saddle point systems [pdf]

Tyrone Rees and Jennifer Scott. Numer. Lin. Alg. Applics., 25:e2103, 2018. DOI: 10.1002/nla.2103

2017

- Numerically aware orderings for sparse symmetric indefinite linear systems [pdf]

Jonathan Hogg, Jennifer Scott and Sue Thorne. ACM Trans. Math. Softw., 44, Number 2, Article 13, 22 pages, 2017. DOI: 10.1145/3104991. - Solving mixed sparse-dense linear least-squares problems by preconditioned iterative methods [pdf]

Jennifer Scott and Miroslav Tuma. SIAM J. Sci. Computing. 39, Number 6, pp A2422-A2437, 2017. DOI: 10.1137/16M1108339. - On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems [pdf]

Jennifer Scott. SIAM J. Sci. Computing, 39, Number 4, pp C319-C339, 2017. DOI: 10.1137/16M1065380. - Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners [pdf]

Jennifer Scott and Miroslav Tuma. Numer. Lin. Alg. Applics., 24:e2099, 2017. DOI: 10.1002/nla.2099. - The state-of-the-art of preconditioners for sparse linear least-squares problems [pdf]

Nick Gould and Jennifer Scott. ACM Trans. Math. Softw., 43, Number 4, Article 36, 35 pages, 2017. DOI: 10.1145/3014057

2016

- Preconditioning of linear least squares by robust incomplete factorization for implicitly held normal equations [pdf]

Jennifer Scott and Miroslav Tuma. SIAM J. Sci. Computing, 38, Number 6, pp C603--C623, 2016. - A sparse symmetric indefinite direct solver for GPU architectures [pdf]

Jonathan Hogg, Evgueni Ovtchinnikov and Jennifer Scott. ACM Trans. Math. Softw., 42, Number 1, Article 1, 25 pages, 2016. DOI: 10.1145/2756548. - A note on performance profiles for benchmarking software [pdf]

Nick Gould and Jennifer Scott. ACM Trans. Math. Softw., 43, Number 2, Article 15, 5 pages, 2016. DOI: 10.1145/2950048. - Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver [pdf]

Peter Dunning, Evgueni Ovtchinnikov, Jennifer Scott and Alicia Kim. Inter. J. Numer. Method. Engng, 2016. DOI: 10.1002/nme.5203

2015

- On the use of suboptimal matchings for scaling and ordering sparse symmetric matrices [pdf]

Jonathan Hogg and Jennifer Scott. Numer. Lin. Alg. Applics., 22, pp 648--663, 2015. DOI: 10.1002/nla.1978

2014

- HSL_MI28: an efficient and robust limited-memory incomplete Cholesky factorization code [pdf]

Jennifer Scott and Miroslav Tuma. ACM Trans. Math. Softw., 40, Article 24, 19 pages, 2014 - On signed incomplete Cholesky factorization preconditioners for saddle-point systems [pdf]

Jennifer Scott and Miroslav Tuma. SIAM J. Sci. Computing, 36, pp A2984-A3010, 2014. - Level-based heuristics and hill climbing for the antibandwidth maximization problem [pdf]

Jennifer Scott and Yifan Hu. Numer. Lin. Alg. Applics., 21, pp 51-67, 2014. - On positive semidefinite modification schemes for incomplete Cholesky factorization [pdf]

Jennifer Scott and Miroslav Tuma. SIAM J. Sci. Computing, 36, pp A609-A633, 2014. - Compressed threshold pivoting for sparse symmetric indefinite systems [pdf]

Jonathan Hogg and Jennifer Scott. SIAM J. Matrix Anal. Appl., 35, pp 783-817, 2014.

2013

- Chebychev acceleration of iterative refinement [pdf]

Mario Arioli and Jennifer Scott. Numer. Alg., 2013. DOI 10.1007/s11075-013-9750-7. - Pivoting strategies for tough sparse indefinite systems [pdf]

Jonathan Hogg and Jennifer Scott. ACM Trans. Math. Softw., 40, Article 4, 19 pages, 2013. - Optimal weighted matchings for rank deficient sparse matrices [pdf]

Jonathan Hogg and Jennifer Scott. SIAM J. Matrix Anal. Applic., 34, pp 1431-1447, 2013. - New parallel sparse direct solvers for multicore archiectures [pdf]

Jonathan Hogg and Jennifer Scott. Algorithms, 6, 702-725, 2013. - An efficient analyse phase for element problems [pdf]

Jonathan Hogg and Jennifer Scott. Numer. Lin. Alg. Applics., 20, pp 397-412, 2013. DOI: 10.1002/nla.1810

2012

- A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints [pdf]

P. A. Browne, C. Budd, N. I. M. Gould, H. A. Kim and J. A. Scott. Inter. J. Numer. Meth. Engng, 92, pp 1026-1043, 2013.

2011

- The importance of structure in incomplete factorization preconditioners [pdf]

Jennifer Scott and Miroslav Tuma. BIT 51, pp 385–404, 2011. - Partial factorization of a dense symmetric indefinite matrix [pdf]

John Reid and Jennifer Scott. ACM Trans. Math. Softw., 38, Article 10, 19 pages, 2011.

2010

- Scaling and pivoting in an out-of-core sparse direct solver [pdf]

Jennifer Scott. ACM Trans. Math. Softw., 37, Article 19, 23 pages, 2010. - A note on fast approximate minimum degree orderings for matrices with some dense rows [pdf]

H. Sue Dollar and Jennifer Scott. Numer. Lin. Alg. Applics., 17, pp 43-55, 2010. - A fast and robust mixed precision solver for the solution of sparse symmetric linear systems [pdf]

Jonathan Hogg and Jennifer Scott. ACM Trans. Math. Softw., 37, Article 17, 24 pages, 2010. - Design of a multicore Cholesky factorization using DAGs [pdf]

Jonathan Hogg, John Reid and Jennifer Scott. SIAM J. Sci. Comput., 32, pp 3627-3649, 2010. - HSL_MI20: an efficient AMG preconditioner for finite element problems in 3D [pdf]

Jonathan Boyle, Milan Mihajlovic and Jennifer Scott. Inter. J. Numer. Meth. Engng, 82, pp 64-98, 2010.

2009

- An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems {pdf]

John Reid and Jennifer Scott. Inter. J. Numer. Meth. Engng, 77, pp 901-921, 2009. - Algorithm 891: a virtual memory system in Fortran [pdf]

John Reid and Jennifer Scott. ACM Trans. Math. Softw., 36, Article 5, 12 pages, 2009. - An out-of-core sparse Cholesky solver [pdf]

John Reid and Jennifer Scott. ACM Trans. Math. Softw., 36, Article 9, 36 pages, 2009.

2007

- A numerical evaluation of sparse direct symmetric solvers for the solution of large sparse, symmetric linear systems of equations [pdf]

Nicholas Gould, Yifan Hu and Jennifer Scott. ACM Trans. Math. Softw., 33, Article 10, 32 pages, 2007. - Experiences of sparse direct symmetric solvers [pdf]

Yifan Hu and Jennifer Scott. ACM Trans. Math. Softw., 33, Article 18, 28 pages, 2007.

2006

- A frontal solver for the 21st century [pdf]

Jennifer Scott. Commun. Numer. Meth. Engng, 22, pp 1015–1029, 2006. - Reducing the total bandwidth of a sparse unsymmetric matrix [pdf]

John Reid and Jennifer Scott. SIAM J. Matrix Anal. Appl. 28, pp 805-821, 2006.

2005

- Ordering techniques for singly bordered block diagonal forms for unsymmetric parallel sparse direct solvers [pdf]

Yifan Hu and Jennifer Scott. Numer. Lin. Alg. Applics., 12, pp 877-894, 2005. - Stabilized bordered block diagonal forms for parallel sparse solvers [pdf]

Iain Duff and Jennifer Scott. Parallel Comput., 31, pp 275-289, 2005. - Multilevel hybrid spectral element ordering algorithms [pdf]

Jennifer Scott. Commun. Numer. Meth. Engng, 21, pp 233-245, 2005.

2004

- A parallel direct solver for large sparse highly unsymmetric linear systems [pdf]

Iain Duff and Jennifer Scott. ACM Trans. Math. Softw., 30, pp 95-117, 2004. - A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations [pdf]

Nicholas Gould and Jennifer Scott. ACM Trans. Math. Softw., 30, pp 300-325, 2004.

2003

- Parallel frontal solvers for large sparse linear systems [pdf]

Jennifer Scott. ACM Trans. Math. Softw., 29, pp 395-417, 2003.

2002

- Implementing Hager's exchange methods for matrix profile reduction [pdf]

John Reid and Jennifer Scott. ACM Trans. Math. Softw., 28, pp 1-15, 2002.

2001

- A parallel frontal solver for finite element applications [pdf]

Jennifer Scott. Inter. J. Numer. Meth. Engng., 50, pp 1131-1144, 2001. - Reversing the row order for the row-by-row frontal solver [pdf]

John Reid and Jennifer Scott

Numer. Lin. Alg. Applics, 8, pp 1-6, 2001. - Two-stage ordering for unsymmetric parallel row-by-row frontal solvers [pdf]

Jennifer Scott. Computers in Chemical Engineering, 25, pp 323-332, 2001. - The design of a portable parallel frontal solver for chemical process engineering problems [pdf]

Jennifer Scott. Computers in Chemical Engineering, 25, pp 1699-1709, 2001. - A multilevel algorithm for wavefront reduction [pdf]

Yifan Hu and Jennifer Scott. SIAM J. Sci. Comput., 23, pp 1352-1375, 2001.

2000

- Row ordering for frontal solvers in chemical process engineering [pdf]

Jennifer Scott. Computers in Chemical Engineering, 24, pp 1865-1880, 2000.

1999

- On ordering elements for a frontal solver [pdf]

Jennifer Scott. Commun. Numer. Meth. Engng, 15, pp 309-323, 1999. - Ordering symmetric sparse matrices for small wavefront and profile [pdf]

John Reid and Jennifer Scott. Inter. J. Numer. Meth. Engng., 45, pp 1737-1755, 1999. - A new row ordering strategy for frontal solvers [ pdf]

Jennifer Scott. Numer. Lin. Alg. Applics, 6, pp 1-23, 1999. - A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications [pdf]

Iain Duff and Jennifer Scott. ACM Trans. Math. Softw., 25, pp 404-424, 1999.

1998

- Sparse approximate-inverse preconditioners using norm-minimization techniques[pdf]

Nicholas Gould and Jennifer Scott. SIAM J. Sci. Comput. 19, pp 605-625, 1998. - Performance issues for frontal schemes on a cache-based high performance computer [pdf]

K. Andrew Cliffe, Iain Duff and Jennifer Scott. Inter. J. Numer. Meth. Engng., 40, pp 127-143, 1998.

1996

- The design of a new frontal code for solving sparse unsymmetric systems [ pdf]

Iain Duff and Jennifer Scott. ACM Trans. Math. Softw., 22, pp 30-45, 1996. - Element resequencing for use with a multiple front solver [pdf]

Jennifer Scott. Inter. J. Numer. Meth. Engng., 39, pp 3999-4020, 1996. - A mathematical model of a biosensor [pdf]

S. Jones, B. Jumarhon, S. McKee and J. A. Scott. J. Engng. Math., 30, pp 321-337, 1996.

1995

- An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices [pdf]

Jennifer Scott. ACM Trans. Math. Softw., 21, pp 423-475, 1995.

1993

- Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration [pdf] [Corrigendum pdf]

Iain Duff and Jennifer Scott. ACM Trans. Math. Softw., 19, pp 137-159, 1993.

1991

- The factorization of sparse symmetric indefinite equations [pdf]

Nicholas Gould, Iain Duff, John Reid, Jennifer Scott and Katherine Turner. IMA J. Numer. Anal. 11, pp 181-204, 1991.

1989

- The use of profile algorithms with a frontal code [pdf]

Iain Duff, John Reid and Jennifer Scott. Inter. J. Numer. Meth. Engng., 28, pp 2555-2568, 1989.

1988

- A finite element model of heat transport in the human eye [pdf]

Jennifer Scott. Physics in Medicine and Biology 33, pp 227-241, 1988. - The computation of temperature rises in the human eye induced by infra-red radiation [pdf]

Jennifer Scott. Physics in Medicine and Biology 33, pp 243-257, 1988. - On the exact order of convergence of discrete methods for Volterra-type equations [pdf]

Jennifer Dixon (Scott) and Sean McKee. IMA J. Numer. Anal. 8, pp 511-515, 1988.

1987

- A nonlinear weakly singular Volterra integral equation arising from a reaction-diffusion study in a small cell [pdf]

Jennifer Dixon (Scott). J. Comput. Appl. Math. 18, pp 289-305, 1987.

1986

- Weakly singular discrete Gronwall inequalities [pdf]

Jennifer Dixon (Scott) and Sean McKee. ZAMM 66, pp 535-544, 1986. - Generalized reducible quadrature methods for Volterra integral and integro-differential equations [pdf]

Jennifer Dixon (Scott). J. Comput. Appl. Math. 16, pp 27-42, 1986. - Convergence analysis of discretization methods for nonlinear first kind Volterra integral equations

[pdf]

Jennifer Dixon (Scott), Sean McKee and Rolf Jetsch. Numer. Math. 49, pp 67-80, 1986.

1985

- A unified approach to convergence analysis for discretization methods for Volterra equations [pdf]

Jennifer Dixon (Scott) and Sean McKee. IMA J. Numer. Anal. 5, pp 41-57, 1985. - On the order of the error in discretization methods for weakly singular second kind Volterra equations with non-smooth solutions [pdf]

Jennifer Dixon (Scott). BIT 25, pp 624-634, 1985.

1984

- Repeated integral inequalities [pdf]

Jennifer Dixon (Scott) and Sean McKee. IMA J. Numer. Anal. 4, pp 99-107, 1984.

1983

- A numerical solution of Lighthill's equation for the surface temperature distribution of a projectile [pdf]

N. B. Franco, S. McKee, and J. A. Dixon (Scott). Mat. Aplic. Comp. 2, pp 257-271, 1983.

**Articles in edited proceedings**

- The design of a new out-of-core multifrontal solver

John Reid and Jennifer Scott

PARA 2006 Conference Proceedings, Springer Lecture Notes in Computer Science, 2007. - An evaluation of sparse direct symmetric solvers: an introduction and preliminary findings

[Article pdf]

Jennifer Scott, Yifan Hu and Nicholas Gould

PARA 2004 Conference Proceedings, Springer Lecture Notes in Computer Science, 2005. - Sparse direct methods: an introduction

Jennifer Scott

Electronic Structure and Physical Properties of Solids editor H. Dreysee. Springer Verlag Lecture Notes in Physics, 2000. - MA62 - A frontal code for sparse positive-definite symmetric systems from finite-element applications

Iain Duff and Jennifer Scott

Innovative Computational Methods for Structural Mechanics, editors M. Papadrakakis and B.H.V. Topping, 1999. - A comparison of frontal software with other Harwell Subroutine Library sparse direct solvers

Iain Duff and Jennifer Scott

High Performance Solution to Structured Matrix Problems, editors Arbenz, Paprzycki, Sameh, and Sarin, 1998. - The use of multiple fronts in Gaussian elimination

Iain Duff and Jennifer Scott

Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, editor J. Lewis, SIAM Press, pp 567-571, 1994. - Computing selected eigenvalues of sparse unsymmetric matrices

Iain Duff and Jennifer Scott

ERCIM Workshop Report ERCIM-92-W002, pp 53-59, 1992. - A unified analysis of discretization methods for Volterra-type equations

Jennifer Dixon (Scott)

Constructive Methods for the Practical Treatment of Integral Equations, editors G. Hammerlin and K. H. Hoffman, Birkhauser Verlag, pp 244-255, 1985.

Author or co-author of the following packages that are part of the HSL mathematical software library.

EA: Eigenvalues and eigenvectors of real symmetric matrices

- EA16 - Compute selected eigenpairs using rational Lanczos method

EB: Eigenvalues and eigenvectors of general matrices

MA: Linear systems

- MA42- Sparse unsymmetric system: out-of-core frontal method
- HSL_MA42_ELEMENT- Unsymmetric finite-element system: out-of-core frontal method
- HSL_MA42- Sparse unsymmetric system: out-of-core frontal method
- MA43- Sparse unsymmetric system: row-by-row frontal method
- MA52- Sparse unsymmetric finite-element system: out-of-core multiple front method
- MA62- Sparse symmetric finite-element system: out-of-core frontal method
- HSL_MA64- Indefinite symmetric full matrix: partial or complete factorization and solution
- MA72- Sparse symmetric finite-element system: out-of-core multiple front method
- HSL_MA74- Unsymmetric full matrix: partial or complete factorization and solution
- HSL_MA77- Sparse symmetric system: multifrontal out of core
- HSL_MA78- Sparse unsymmetric finite-element system: multifrontal out of core
- HSL_MA79- Sparse symmetric system: mixed precision
- HSL_MA85- Sparse diagonally-weighted linear least squares solver
- HSL_MA86- Sparse solver for real and complex indefinite matrices using OpenMP
- HSL_MA87- Sparse Cholesky solver for real/complex matrices using OpenMP
- HSL_MA97- Bit-compatible sparse symmetric indefinite linear solver

MC: Computations with real matrices and vectors

- HSL_MC34- Sparse symmetric structure: expand from lower triangle
- MC44- Unassembled finite-element matrix: generate the element or supervariable connectivity graph
- MC53- Generate an ordering for finite-element matrices within a subdomain
- MC57- Assemble a set of finite-element matrices
- MC59- Sort a sparse matrix to an ordering by columns
- MC60- Sparse symmetric pattern: reduce the profile and wavefront
- MC61- Straightforward interface to MC60
- MC62- Generate a row ordering for a row-by-row frontal solver
- MC63- Generate an element assembly ordering for a frontal solver
- MC67- Refine a profile-reducing permutation of a symmetric matrix
- HSL_MC68- Symmetric sparse matrix: compute elimination orderings
- HSL_MC73- Sparse symmetric matrix: compute Fiedler vector and permute to reduce the profile and wavefront
- HSL_MC80- Sparse symmetric matrix: matching-based ordering and scaling
- HSL_MC81 - Randomized methods for low-rank matrix approximation

ME: Solution of complex linear systems and other calculations for complex matrices

- ME42- Sparse unsymmetric system: out-of-core frontal method
- ME43- Sparse unsymmetric system: row-by-row frontal method
- ME62- Sparse Hermitian or complex symmetric finite-element system: out-of-core frontal method

*See also*

- HSL_MA42_ELEMENT- (Unsymmetric finite-element system)
- HSL_MA86- (Parallel sparse symmetric indefinite/Hermitian)
- HSL_MA87- (Parallel sparse Cholesky)
- HSL_MA97 - (Bit-compatible parallel sparse symmetric/Hermitian)

MI: Iterative methods for sparse matrices

- MI11- Unsymmetric system: incomplete LU factorization
- MI12- Unsymmetric system: approximate-inverse preconditioner
- HSL_MI20- Unsymmetric system: algebraic multigrid preconditioner
- MI21- Symmetric positive-definite system: conjugate gradient method
- MI23- Unsymmetric system: CGS (conjugate gradient squared) method
- MI24- Unsymmetric system: GMRES (generalized minimal residual) method
- MI25- Unsymmetric system: BiCG (BiConjugate Gradient) method
- MI26- Unsymmetric system: BiCGStab (BiConjugate Gradient Stabilized) method
- HSL_MI28- Symmetric system: incomplete Cholesky factorization
- HSL_MI30- Symmetric indefinite saddle-point system: signed incomplete Cholesky factorization
- HSL_MI35 - Sparse least squares: incomplete factorization preconditioner

MP: MPI dependant packages

- HSL_MP42- Unsymmetric finite-element system: multiple-front method, element entry
- HSL_MP43- Sparse unsymmetric system: multiple-front method, equation entry
- HSL_MP48- Sparse unsymmetric system: parallel direct method
- HSL_MP62 - Symmetric finite-element system: multiple-front method

OF: File management

- HSL_OF01- Fortran virtual memory

Technical **Reports/Preprints (not published elsewhere in revised form)**

2024

- On incomplete Cholesky factorizations in half precision arithmetic.

[RAL Preprint pdf]

J. A. Scott and M. Tuma

Preprint STFC-P--2024-002

- Approximating large-scale Hessian matrices using secant equations.

[RAL Preprint pdf]

J.M. Fowkes, N.I.M. Gould and J. A. Scott

Preprint STFC-P--2024-001

2023

- HSL@60: a brief history of the HSL mathematical software library

[RAL Technical Report pdf]

J. A. Scott

Technical Report RAL-TR-2023-002

2019

- Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints

[RAL Technical Report pdf]

N.I.M. Gould, T. Rees and J.A. Scott

Technical Report RAL-TR-2019-001

2017

- A higher order method for solving nonlinear least-squares problems

[RAL Technical Report pdf]

N.I.M. Gould, T. Rees and J.A. Scott

Technical Report RAL-P-2017-010 - Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems

[RAL Technical Report pdf]

N.I.M. Gould, T. Rees and J.A. Scott

Technical Report RAL-P-2017-009

2016

- Nested dissection revisited

[RAL Technical Report pdf]

Cleve Ashcraft, Iain Duff, Jonathan Hogg, Jennifer Scott and Sue Thorne

Technical Report RAL-TR-2016-004

2015

- The state-of-the-art of preconditioners for sparse linear least-squares problems: the complete results

[RAL Technical Report pdf]

Nicholas Gould and Jennifer Scott

Technical Report RAL-TR-2015-009 (corrected)

2014

- On the efficient scaling of sparse symmetric matrices using an auction algorithm

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-P-2014-002 - Experiments using incomplete Cholesky factorization preconditioners for saddle-point systems arising in interior-point methods

[RAL Technical Report pdf]

Jennifer Scott

Technical Report RAL-TR-2014-011

2012

- On the effects of scaling on the performance of Ipopt

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-P-2012-009 - Achieving bit compatibility in sparse direct solvers

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-P-2012-005 - Numerical Analysis Group Progress Report January 2010 - December 2011

[RAL Technical Report pdf]

Jennifer Scott (editor)

Technical Report RAL-TR-2012-001

2011

- HSL_MA97 : a bit-compatible multifrontal code for sparse symmetric systems

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-TR-2011-024 - Guidelines for the development of HSL software, 2011 version

[RAL Technical Report pdf]

Jonathan Hogg, John Reid and Jennifer Scott

Technical Report RAL-TR-2011-015

2010

- A modern analyse phase for sparse tree-based direct methods

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-TR-2010-031 - An indefinite sparse direct solver for large problems on multicore machines

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-TR-2010-011 - A note on the solve phase of a multicore solver

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-TR-2010-004 - Numerical Analysis Group Progress Report: January 2008 - December 2009

[RAL Technical Report pdf]

Jennifer Scott (editor)

Technical Report RAL-TR-2010-001

2009

- A note on a simple constrained ordering for saddle-point systems

[RAL Technical Report pdf]

Jennifer Scott

Technical Report RAL-TR-2009-007

2008

- An efficient out-of-core sparse symmetric indefinite direct solver

[RAL Technical Report pdf]

John Reid and Jennifer Scott

Technical Report RAL-TR-2008-024 - The effects of scalings on the performance of a sparse symmetric indefinite solver

[RAL Technical Report pdf]

Jonathan Hogg and Jennifer Scott

Technical Report RAL-TR-2008-007 - Numerical Analysis Group Progress Report: January 2006 - December 2007

[RAL Technical Report pdf]

Jennifer Scott

Technical Report RAL-TR-2008-001

2007

- An approximate minimum degree algorithm for matrices with dense rows

[RAL Technical Report pdf]

Patrick Amestoy, Sue Dollar, John Reid and Jennifer Scott

Technical Report RAL-TR-2007-020

2006

- Towards an automatic ordering for a symmetric sparse direct solver

[RAL Technical Report pdf]

Iain Duff and and Jennifer Scott

Technical Report RAL-TR-2006-001

2004

- MA42_ELEMENT - a state-of-the-art frontal solver for finite-element applications

[RAL Technical Report pdf]

Jennifer Scott

Technical Report RAL-TR-2004-026

2000

- The design of a block rational Lanczos code with partial reorthogonalization and implicit restarting

[RAL Technical Report pdf]

Karl Meerbergen and Jennifer Scott

Technical Report RAL-TR-2000-011

1997

- Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier-Stokes equations

[RAL Technical Report pdf]

RB Lehoucq and JA Scott

Technical Report RAL-TR-1997-058 - Exploiting zeros in frontal solvers

[RAL Technical Report pdf]

Jennifer Scott

Technical Report RAL-TR-1997-031 - MA62: A frontal code for sparse positive definite symmetric systems from finite element applications

[RAL Technical Report pdf]

Iain Duff and Jennifer Scott

Technical Report RAL-TR-1997-012

1996

- An evaluation of subspace iteration software for sparse nonsymmetric egenproblems

[RAL Technical Report pdf]

RB Lehoucq and JA Scott

Technical Report RAL-TR-1996-022 - An evaluation of Arnoldi based software for sparse nonsymmetric eigenproblems

[RAL Technical Report pdf]

RB Lehoucq and JA Scott

Technical Report RAL-TR-1996-023

1993

- MA42 - A new frontal code for solving sparse unsymmetric systems

[RAL Technical Report pdf]

Iain Duff and Jennifer Scott

Technical Report RAL-TR-1993-064