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

Autor:	Martin B. van Gijzen, Jens-Peter M. Zemke, Gerard L. G. Sleijpen
Rok vydání:	2014
Předmět:	Algebra and Number Theory Basis (linear algebra) Iterative method Applied Mathematics Dimensionality reduction Linear system Decomposition (computer science) Krylov subspace Residual Algorithm Mathematics
Zdroj:	Numerical Linear Algebra with Applications. 22:1-25
ISSN:	1070-5325
DOI:	10.1002/nla.1935
Popis:	We 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.
Databáze:	OpenAIRE
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