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Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse
Li, Wen1; Chen, Yanmei1,2; Vong, Seakweng3; Luo, Qilun1
2018-10
Source PublicationNUMERICAL ALGORITHMS
ISSN1017-1398
Volume79Issue:2Pages:657-677
Abstract

In this paper, we consider the perturbation of the orthogonal projection and the generalized inverse for an n x n matrix A and present some perturbation bounds for the orthogonal projections on the rang spaces of A and A, respectively. A combined bound for the orthogonal projection on the rang spaces of A and A is also given. The proposed bounds are sharper than the existing ones. From the combined bounds of the orthogonal projection on the rang spaces of A and A, we derived new perturbation bounds for the generalized inverse, which always improve the existing ones. The combined perturbation bound for the orthogonal projection and the generalized inverse is also given. Some numerical examples are given to show the advantage of the new bounds.

KeywordSingular Value Decomposition Orthogonal Projection Perturbation Generalized Inverse
DOI10.1007/s11075-018-0473-7
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000445494100015
PublisherSPRINGER
The Source to ArticleWOS
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
2.School of Mathematics and Systems ScienceGuangdong Polytechnic Normal UniversityGuangzhouChina
3.Department of MathematicsUniversity of MacauMacauChina
Recommended Citation
GB/T 7714
Li, Wen,Chen, Yanmei,Vong, Seakweng,et al. Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse[J]. NUMERICAL ALGORITHMS,2018,79(2):657-677.
APA Li, Wen,Chen, Yanmei,Vong, Seakweng,&Luo, Qilun.(2018).Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse.NUMERICAL ALGORITHMS,79(2),657-677.
MLA Li, Wen,et al."Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse".NUMERICAL ALGORITHMS 79.2(2018):657-677.
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