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

Kentaro Moriya, Takashi Nodera

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationLecture Notes in Computer Science
EditorsO. Gervasi, M.L. Gavrilova, V. Kumar, A. Lagana, H.P. Lee, Y. Mun, D. Taniar, C.J.K. Tan
Pages978-988
Number of pages11
Volume3483
EditionIV
Publication statusPublished - 2005
EventInternational Conference on Computational Science and Its Applications - ICCSA 2005 - , Singapore
Duration: 2005 May 92005 May 12

Other

OtherInternational Conference on Computational Science and Its Applications - ICCSA 2005
CountrySingapore
Period05/5/905/5/12

Fingerprint

Nonlinear systems
Costs
Experiments

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Moriya, K., & Nodera, T. (2005). Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems. In O. Gervasi, M. L. Gavrilova, V. Kumar, A. Lagana, H. P. Lee, Y. Mun, D. Taniar, ... C. J. K. Tan (Eds.), Lecture Notes in Computer Science (IV ed., Vol. 3483, pp. 978-988)

Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems. / Moriya, Kentaro; Nodera, Takashi.

Lecture Notes in Computer Science. ed. / O. Gervasi; M.L. Gavrilova; V. Kumar; A. Lagana; H.P. Lee; Y. Mun; D. Taniar; C.J.K. Tan. Vol. 3483 IV. ed. 2005. p. 978-988.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Moriya, K & Nodera, T 2005, Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems. in O Gervasi, ML Gavrilova, V Kumar, A Lagana, HP Lee, Y Mun, D Taniar & CJK Tan (eds), Lecture Notes in Computer Science. IV edn, vol. 3483, pp. 978-988, International Conference on Computational Science and Its Applications - ICCSA 2005, Singapore, 05/5/9.
Moriya K, Nodera T. Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems. In Gervasi O, Gavrilova ML, Kumar V, Lagana A, Lee HP, Mun Y, Taniar D, Tan CJK, editors, Lecture Notes in Computer Science. IV ed. Vol. 3483. 2005. p. 978-988
Moriya, Kentaro ; Nodera, Takashi. / Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems. Lecture Notes in Computer Science. editor / O. Gervasi ; M.L. Gavrilova ; V. Kumar ; A. Lagana ; H.P. Lee ; Y. Mun ; D. Taniar ; C.J.K. Tan. Vol. 3483 IV. ed. 2005. pp. 978-988
@inproceedings{01c4edb2381d444eb9c65646384d957c,
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",
language = "English",
volume = "3483",
pages = "978--988",
editor = "O. Gervasi and M.L. Gavrilova and V. Kumar and A. Lagana and H.P. Lee and Y. Mun and D. Taniar and C.J.K. Tan",
booktitle = "Lecture Notes in Computer Science",
edition = "IV",

}

TY - GEN

T1 - Breakdown-free ML(k)BiCGStab algorithm for non-hermitian linear systems

AU - Moriya, Kentaro

AU - Nodera, Takashi

PY - 2005

Y1 - 2005

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.

UR - http://www.scopus.com/inward/record.url?scp=24944535419&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944535419&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:24944535419

VL - 3483

SP - 978

EP - 988

BT - Lecture Notes in Computer Science

A2 - Gervasi, O.

A2 - Gavrilova, M.L.

A2 - Kumar, V.

A2 - Lagana, A.

A2 - Lee, H.P.

A2 - Mun, Y.

A2 - Taniar, D.

A2 - Tan, C.J.K.

ER -