Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems

Kentaro Moriya; Takashi Nodera

doi:10.1007/11424925_102

Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems

Kentaro Moriya, Takashi Nodera

Department of Mathematics

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

ML(k)BiCGStab algorithm stabilizes BiCGStab algorithm by using k pseudo Krylov subspaces. However, if k is too large, the computation cost often becomes expensive, and the performance of BiCGStab algorithm is not always improved. In this paper, a new variant of ML(k)BiCGStab algorithm is proposed. In the proposed scheme, k is varied and pseudo Krylov subspaces are recomputed when the Lanczos breakdown occurs. Numerical experiments are reported which indicate that the proposed scheme performs better than the original ML(k)BiCGStab algorithm and BiCGStab algorithm.

Original language	English
Pages (from-to)	978-988
Number of pages	11
Journal	Lecture Notes in Computer Science
Volume	3483
Issue number	IV
DOIs	https://doi.org/10.1007/11424925_102
Publication status	Published - 2005
Event	International Conference on Computational Science and Its Applications - ICCSA 2005 - , Singapore Duration: 2005 May 9 → 2005 May 12

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/11424925_102

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title = "Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems",

abstract = "ML(k)BiCGStab algorithm stabilizes BiCGStab algorithm by using k pseudo Krylov subspaces. However, if k is too large, the computation cost often becomes expensive, and the performance of BiCGStab algorithm is not always improved. In this paper, a new variant of ML(k)BiCGStab algorithm is proposed. In the proposed scheme, k is varied and pseudo Krylov subspaces are recomputed when the Lanczos breakdown occurs. Numerical experiments are reported which indicate that the proposed scheme performs better than the original ML(k)BiCGStab algorithm and BiCGStab algorithm.",

author = "Kentaro Moriya and Takashi Nodera",

year = "2005",

doi = "10.1007/11424925_102",

language = "English",

volume = "3483",

pages = "978--988",

journal = "Lecture Notes in Computer Science",

issn = "0302-9743",

publisher = "Springer Verlag",

number = "IV",

note = "International Conference on Computational Science and Its Applications - ICCSA 2005 ; Conference date: 09-05-2005 Through 12-05-2005",

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AU - Moriya, Kentaro

AU - Nodera, Takashi

PY - 2005

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N2 - ML(k)BiCGStab algorithm stabilizes BiCGStab algorithm by using k pseudo Krylov subspaces. However, if k is too large, the computation cost often becomes expensive, and the performance of BiCGStab algorithm is not always improved. In this paper, a new variant of ML(k)BiCGStab algorithm is proposed. In the proposed scheme, k is varied and pseudo Krylov subspaces are recomputed when the Lanczos breakdown occurs. Numerical experiments are reported which indicate that the proposed scheme performs better than the original ML(k)BiCGStab algorithm and BiCGStab algorithm.

AB - ML(k)BiCGStab algorithm stabilizes BiCGStab algorithm by using k pseudo Krylov subspaces. However, if k is too large, the computation cost often becomes expensive, and the performance of BiCGStab algorithm is not always improved. In this paper, a new variant of ML(k)BiCGStab algorithm is proposed. In the proposed scheme, k is varied and pseudo Krylov subspaces are recomputed when the Lanczos breakdown occurs. Numerical experiments are reported which indicate that the proposed scheme performs better than the original ML(k)BiCGStab algorithm and BiCGStab algorithm.

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JF - Lecture Notes in Computer Science

IS - IV

T2 - International Conference on Computational Science and Its Applications - ICCSA 2005

Y2 - 9 May 2005 through 12 May 2005

ER -

Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems

Abstract

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