Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems

Authors:
Michael Hagemann;Olaf Schenk
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2006

Citing 0
Cited 7

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A numerical evaluation of preprocessing and ILU-type preconditioners for the solution of unsymmetric sparse linear systems using iterative methods

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An auction-based weighted matching implementation on massively parallel architectures

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Pivoting strategies for tough sparse indefinite systems

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Linear-Time Approximation for Maximum Weight Matching

Journal of the ACM (JACM)

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Abstract

Maximum weight matchings have become an important tool for solving highly indefinite unsymmetric linear systems, especially in direct solvers. In this study we investigate the benefit of reorderings and scalings based on symmetrized maximum weight matchings as a preprocessing step for incomplete $\mathrm{LDL^T}$ factorizations. The reorderings are constructed such that the matched entries form $1 \times 1$ or $2 \times 2$ diagonal blocks in order to increase the diagonal dominance of the system. During the incomplete factorization only tridiagonal pivoting is used. We report results for this approach and comparisons with other solution methods for a diverse set of symmetric indefinite matrices, ranging from nonlinear elasticity to interior point optimization.