Downloads provided by UsageCountsParallel Computation of Entries of ${A}^{-1}$
Copyright policy ) Amestoy, Patrick; Duff, Iain S.; L'Excellent, Jean-Yves; Rouet, François-Henry;
Parallel Computation of Entries of ${A}^{-1}$
Summary: 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.
Parallel computing, computational efficiency, Calcul parallèle, sparse matrices, Sparse Linear Algebra, parallel algorithms, Parallel numerical computation, MUMPS, Direct numerical methods for linear systems and matrix inversion, Calcul parallèle, distribué et partagé, Computational methods for sparse matrices, Complexity and performance of numerical algorithms, [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS], [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], distribué et partagé, direct methods for linear system and matrix inversion
Parallel computing, computational efficiency, Calcul parallèle, sparse matrices, Sparse Linear Algebra, parallel algorithms, Parallel numerical computation, MUMPS, Direct numerical methods for linear systems and matrix inversion, Calcul parallèle, distribué et partagé, Computational methods for sparse matrices, Complexity and performance of numerical algorithms, [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS], [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], distribué et partagé, direct methods for linear system and matrix inversion
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10% views 34 downloads 28 - 34views28downloads
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This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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