Behavior of the Correction Equations in the Jacobi–Davidson Method

Behavior of the Correction Equations in the Jacobi–Davidson Method

The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically,...

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Main Authors: Yuan Kong, Yong Fang
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/5169362
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spelling doaj-70d3c588c2de445fbf905b02208c7d112020-11-24T22:12:41ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/51693625169362Behavior of the Correction Equations in the Jacobi–Davidson MethodYuan Kong0Yong Fang1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.http://dx.doi.org/10.1155/2019/5169362
collection DOAJ
language English
format Article
sources DOAJ
author Yuan Kong
Yong Fang
spellingShingle Yuan Kong
Yong Fang
Behavior of the Correction Equations in the Jacobi–Davidson Method
Mathematical Problems in Engineering
author_facet Yuan Kong
Yong Fang
author_sort Yuan Kong
title Behavior of the Correction Equations in the Jacobi–Davidson Method
title_short Behavior of the Correction Equations in the Jacobi–Davidson Method
title_full Behavior of the Correction Equations in the Jacobi–Davidson Method
title_fullStr Behavior of the Correction Equations in the Jacobi–Davidson Method
title_full_unstemmed Behavior of the Correction Equations in the Jacobi–Davidson Method
title_sort behavior of the correction equations in the jacobi–davidson method
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.
url http://dx.doi.org/10.1155/2019/5169362
work_keys_str_mv AT yuankong behaviorofthecorrectionequationsinthejacobidavidsonmethod
AT yongfang behaviorofthecorrectionequationsinthejacobidavidsonmethod
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