Heuristics for a Matrix Symmetrization Problem

Uçar, Bora

doi:10.1007/978-3-540-68111-3_75

Cited by 2 publications

(18 citation statements)

References 11 publications

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“…Uçar [19] investigates the second objective for (0, 1)matrices. Referring to two earlier studies [5,7], he notes that the problem is NP-complete and proposes iterative improvement based heuristics.…”

Section: Introductionmentioning

confidence: 99%

“…As this is a multi-objective optimization problem with one of the objectives being NP-complete, the whole problem is NP-complete. We propose a heuristic by combining the algorithms from MC64 and earlier work [19]. We first permute and scale the matrix using MC64.…”

Section: Introductionmentioning

confidence: 99%

“…The subset is chosen so that it would be helpful for numerical pivoting. By choosing all nonzero entries of D r AQ MC64 D c to be in that subset, one recovers a pattern symmetrizing matching [19]; by choosing all nonzero entries of |D r AQ MC64 D c | that are one to be in that subset one recovers an MC64 matching (with improved pattern symmetry). This is tied to a parameter to strike a balance between numerical issues and pattern symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…We introduce the notation and give some background on bipartite graphs and MC64 in Section 2. Since we build upon, extend, and improve the earlier work [19], we summarize it in the same section. This section also contains a brief summary of the standard preprocessing phase of sparse direct solvers for unsymmetric matrices.…”

Section: Introductionmentioning

confidence: 99%

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Matrix symmetrization and sparse direct solvers

Portase¹,

Uçar²

2020

2020 Proceedings of the SIAM Workshop on Combinatorial Scientific Computing

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We investigate algorithms for finding column permutations of sparse matrices in order to have large diagonal entries and to have many entries symmetrically positioned around the diagonal. The aim is to improve the memory and running time requirements of a certain class of sparse direct solvers. We propose efficient algorithms for this purpose by combining two existing approaches and demonstrate the effect of our findings in practice using a direct solver. We show improvements in a number of components of the running time of a sparse direct solver with respect to the state of the art on a diverse set of matrices.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Matrix symmetrization and sparse direct solvers

Portase¹,

Uçar²

2020

2020 Proceedings of the SIAM Workshop on Combinatorial Scientific Computing

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“…We assume that both A and S ∈ {S r , S l } are sparse and nonsymmetric, with S having a user-defined sparsity structure. The sparse ASSS preconditioner is obtained by first applying a nonsymmetric permutation and scaling and then solving a sparse overdetermined linear least squares (LLS) problem to obtain S. Similar approaches for dense symmetrizers [8] or algorithms for improving the structural symmetry in the context of sparse direct solvers, as proposed in [26,30], do not have the latter property.…”

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confidence: 99%

A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers

Manguoğlu¹,

Mehrmann²

2021

etna

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We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the norm of the skew-symmetric part relative to the rest and makes the main diagonal of the coefficient matrix as close to the identity as possible so that the preconditioned system is as close to a shifted skew-symmetric matrix as possible. The preconditioned system is then solved via a particular Minimal Residual Method for Shifted Skew-Symmetric Systems (MRS). This leads to a two-level (inner and outer) iterative scheme where the MRS has short-term recurrences and satisfies an optimality condition. A preconditioner for the inner system is designed via a skew-symmetry-preserving deflation strategy based on the skew-Lanczos process. We demonstrate the robustness of the proposed scheme on sparse matrices from various applications.

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Heuristics for a Matrix Symmetrization Problem

Cited by 2 publications

References 11 publications

Matrix symmetrization and sparse direct solvers

Matrix symmetrization and sparse direct solvers

A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers

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