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An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace

Published online by Cambridge University Press:  28 May 2015

Akira Imakura
Akira Imakura*
Affiliation:
Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai Tsukuba-city, Ibaraki 305-8573, Japan
*
Corresponding author. Email address: [email protected]
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Abstract

Subspace projection methods based on the Krylov subspace using powers of a matrix A have often been standard for solving large matrix computations in many areas of application. Recently, projection methods based on the extended Krylov subspace using powers of A and A−1 have attracted attention, particularly for functions of a matrix times a vector and matrix equations. In this article, we propose an efficient algorithm for constructing an orthonormal basis for the extended Krylov subspace. Numerical experiments indicate that this algorithm has less computational cost and approximately the same accuracy as the traditional algorithm.

Keywords

65F1065F2565F3015A06Extended Krylov subspaceKrylov subspacesubspace projection methodsorthonormal basislinear systems
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 3 , August 2014 , pp. 267 - 282
Copyright
Copyright © Global-Science Press 2014

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