Year: 2014
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 267–282
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.240413.020614a
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 3 : pp. 267–282
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Extended Krylov subspace Krylov subspace subspace projection methods orthonormal basis linear systems.