Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems

SUMMARYWe give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi‐shift quasi‐minimal residual IDR variant. These variants are based on a generalized Hessenberg decomposition. We present a new, more stable way to...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2015-01, Vol.22 (1), p.1-25
Main Authors: van Gijzen, Martin B., Sleijpen, Gerard L. G., Zemke, Jens-Peter M.
Format: Article
Language:English
Subjects:
Algorithms
IDR
IDR(s)
iterative methods
Krylov subspace methods
large sparse nonsymmetric linear systems
Linear algebra
Linear systems
Mathematical analysis
Mathematical models
quasi-minimal residual
Reduction
Subspace methods
Vectors (mathematics)
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Summary:SUMMARYWe give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi‐shift quasi‐minimal residual IDR variant. These variants are based on a generalized Hessenberg decomposition. We present a new, more stable way to compute basis vectors in IDR. Numerical examples are presented to show the effectiveness of these new IDR variants and the new basis compared with existing ones and to other Krylov subspace methods. Copyright © 2014 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.1935