Abstract

In this paper, we consider the computation in parallel of several entries of the inverse of a large sparse matrix. We assume that the matrix has already been factorized by a direct method and that the factors are distributed. Entries are efficiently computed by exploiting sparsity of the right-hand sides and the solution vectors in the triangular solution phase. We demonstrate that in this setting, parallelism and computational efficiency are two contrasting objectives. We develop an efficient approach and show its efficiency on a general purpose parallel multifrontal solver.

Keywords

  1. sparse matrices
  2. direct methods for linear system and matrix inversion
  3. parallel algorithms

MSC codes

  1. 05C50
  2. 65F05
  3. 65F50
  4. 68W10

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: C268 - C284
ISSN (online): 1095-7197

History

Submitted: 14 December 2012
Accepted: 26 February 2015
Published online: 30 April 2015

Keywords

  1. sparse matrices
  2. direct methods for linear system and matrix inversion
  3. parallel algorithms

MSC codes

  1. 05C50
  2. 65F05
  3. 65F50
  4. 68W10

Authors

Affiliations

François-Henry Rouet

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