article

Author: Anshul Gupta

ACM Transactions on Mathematical Software (TOMS), Volume 28, Issue 3

Pages 301 - 324

Published: 01 September 2002 Publication History

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## Abstract

During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.

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## Index Terms

Recent advances in direct methods for solving unsymmetric sparse systems of linear equations

Computing methodologies

Symbolic and algebraic manipulation

Symbolic and algebraic algorithms

Linear algebra algorithms

Mathematics of computing

Mathematical analysis

Numerical analysis

Computations on matrices

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#### Published In

ACM Transactions on Mathematical Software Volume 28, Issue 3

September 2002

91 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/569147

Issue’s Table of Contents

Copyright © 2002 ACM.

#### Publisher

Association for Computing Machinery

New York, NY, United States

#### Publication History

**Published**: 01 September 2002

Published inTOMSVolume 28, Issue 3

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#### Author Tags

- Multifrontal Method
- Parallel Sparse Solvers
- Sparse LU Decomposition
- Sparse Matrix Factorization

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**115**(103780)Online publication date: Nov-2022 - Santhosh AJog C(2022)A monolithic finite element strategy for conjugate heat transferSādhanā10.1007/s12046-022-01991-3
**47**:4Online publication date: 1-Nov-2022 - Farea AÇelebi M(2022)On the evaluation of general sparse hybrid linear solversNumerical Linear Algebra with Applications10.1002/nla.2469
**30**:2Online publication date: 28-Sep-2022 - Potghan NJog C(2022)An ALE‐based finite element strategy for modeling compressible two‐phase flowsInternational Journal for Numerical Methods in Fluids10.1002/fld.5134
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