Volume 4, Issue 3
An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace

Akira Imakura

East Asian J. Appl. Math., 4 (2014), pp. 267-282.

Published online: 2018-02

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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

Extended Krylov subspace Krylov subspace subspace projection methods orthonormal basis linear systems

  • AMS Subject Headings

65F10 65F25 65F30 15A06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-267, author = {Akira Imakura}, title = {An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240413.020614a}, url = {http://global-sci.org/intro/article_detail/eajam/10836.html} }
TY - JOUR T1 - An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace AU - Akira Imakura JO - East Asian Journal on Applied Mathematics VL - 3 SP - 267 EP - 282 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.240413.020614a UR - https://global-sci.org/intro/article_detail/eajam/10836.html KW - Extended Krylov subspace KW - Krylov subspace KW - subspace projection methods KW - orthonormal basis KW - linear systems AB -

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.

Akira Imakura. (1970). An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace. East Asian Journal on Applied Mathematics. 4 (3). 267-282. doi:10.4208/eajam.240413.020614a
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