NDLI: A new quasi-minimal residual method based on a biconjugate A-orthonormalization procedure and coupled two-term recurrences

Content Provider	Springer Nature Link
Author	Zhang, Jianhua Dai, Hua
Copyright Year	2015
Abstract	Recently, some novel variants of Lanczos-type methods were explored that are based on the biconjugate A-orthonormalization process. Numerical experiments coming from some physical problems indicate that these new methods are competitive with or superior to other popular Krylov subspace methods. Among them, the biconjugate A-orthogonal residual (BiCOR) method is the archetype method. However, like the biconjugate gradient (BiCG) method, the BiCOR method often shows irregular convergence behavior which can lead to numerical instability. To overcome this drawback, motivated by the effectiveness and robustness of the quasi-minimal residual (QMR) method, we derive a new QMR-like approach based on the coupled two-term biconjugate A-orthonormalization process and simple recurrences instead of the QR decomposition. Some convergence properties are given, and the special case for solving complex symmetric linear system is considered. Finally, numerical experiments are reported to illustrate the performances of our methods and their preconditioners on linear systems discretizing the Helmholtz equation or taken from Florida Sparse Matrix Collection.
Starting Page	875
Ending Page	896
Page Count	22
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	70
Issue Number	4
e-ISSN	15729265
Language	English
Publisher	Springer US
Publisher Date	2015-02-26
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Complex non-Hermitian matrices QMR method Coupled two-term recurrences BiCOR method Complex symmetric matrices Numeric Computing Algorithms Algebra Theory of Computation Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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