Majorization bounds for SVD
Given an approximating singular subspace of a matrix, in this paper, two kind of majorization type bounds on the singular value errors by the canonical angles between the singular subspaces and its approximations are obtained. From these results, based on the information about approximation accuracies of a pair of approximate singular subspaces, several bounds can be directly obtained to estimate how accurate the approximate singular values are. These results are helpful to understand how approximate singular values converge to the corresponding exact singular values in the projection subspace type algorithms.
KeywordsSingular value Singular vector Majorization
Mathematics Subject Classification65F15 15A18
The authors are grateful to the anonymous referees for their careful reading, useful comments, and suggestions for improving the presentation of this paper. The work of the first author is supported in part by National Natural Science Foundation of China NSFC-11601081 and the research fund for distinguished young scholars of Fujian Agriculture and Forestry University No. xjq201727. The work of the second author is supported in part by National Natural Science Foundation of China Grant NSFC-11601347, and the Shenzhen Infrastructure Project No. JCYJ20170306095959113.