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GMRES convergence bounds that depend on the right-hand-side vector

Abstract:

We consider the convergence of the algorithm GMRES of Saad and Schultz for solving linear equations Bx=b, where B ∈ ℂn × n is nonsingular and diagonalizable, and b ∈ ℂn. Our analysis explicitly includes the initial residual vector r0. We show that the GMRES residual norm satisfies a weighted polynomial least-squares problem on the spectrum of B, and that GMRES convergence reduces to an ideal GMRES problem on a rank-1 modification of the diagonal matrix of eigenvalues of B. Numerical experimen...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1093/imanum/drt025

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
New College
Role:
Author
Publisher:
Oxford University Press
Journal:
IMA Journal of Numerical Analysis More from this journal
Volume:
34
Issue:
2
Pages:
462-479
Publication date:
2013-07-25
DOI:
EISSN:
1464-3642
ISSN:
0272-4979
Keywords:
Pubs id:
pubs:463478
UUID:
uuid:682cdddf-e26c-4540-bb82-37ab23d09648
Local pid:
pubs:463478
Source identifiers:
463478
Deposit date:
2017-11-27

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