Experiences of sparse direct symmetric solvers

We recently carried out an extensive comparison of the performance of state-of-the-art sparse direct solvers for the numerical solution of symmetric linear systems of equations. Some of these solvers were written primarily as research codes while others have been developed for commercial use. Our experiences of using the different packages to solve a wide range of problems arising from real applications were mixed. In this paper, we highlight some of these experiences with the aim of providing advice to both software developers and users of sparse direct solvers. We discuss key features that a direct solver should offer and conclude that while performance is an essential factor to consider when choosing a code, there are other features that a user should also consider looking for that vary significantly between packages.

[1]  John G. Lewis,et al.  Accurate Symmetric Indefinite Linear Equation Solvers , 1999, SIAM J. Matrix Anal. Appl..

[2]  Yuefan Deng,et al.  New trends in high performance computing , 2001, Parallel Computing.

[3]  Jennifer A. Scott,et al.  A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications , 1999, TOMS.

[4]  Sivan Toledo,et al.  The design and implementation of a new out-of-core sparse cholesky factorization method , 2004, TOMS.

[5]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2002, Future Gener. Comput. Syst..

[6]  Timothy A. Davis,et al.  Modifying a Sparse Cholesky Factorization , 1999, SIAM J. Matrix Anal. Appl..

[7]  E. Ng,et al.  An E cient Algorithm to Compute Row andColumn Counts for Sparse Cholesky Factorization , 1994 .

[8]  Iain S. Duff,et al.  MA57---a code for the solution of sparse symmetric definite and indefinite systems , 2004, TOMS.

[9]  Jack Dongarra,et al.  Numerical Linear Algebra for High-Performance Computers , 1998 .

[10]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[11]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[12]  John K. Reid,et al.  The Multifrontal Solution of Indefinite Sparse Symmetric Linear , 1983, TOMS.

[13]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[14]  Nicholas I. M. Gould,et al.  A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations , 2007, TOMS.

[15]  Nicholas I. M. Gould,et al.  A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations , 2004, TOMS.

[16]  Florin Dobrian,et al.  The design of sparse direct solvers using object-oriented techniques , 1999 .

[17]  Cleve Ashcraft,et al.  SPOOLES: An Object-Oriented Sparse Matrix Library , 1999, PPSC.

[18]  Jack J. Dongarra,et al.  Automated empirical optimizations of software and the ATLAS project , 2001, Parallel Comput..

[19]  John K. Reid,et al.  Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems , 1996, TOMS.

[20]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .