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Volume 19, Issue 1
New Perturbation Analysis of Generalized Singular Values of Grassmann Matrix Pairs with Arbitrary Permutation

Yujie Wang, Lei Zhu & Weiwei Xu

DOI: 10.4208/JICS-2024-002

J. Info. Comput. Sci. , 19 (2024), pp. 15-40.

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  • Abstract

In this paper we give new perturbation analysis of generalized singular values of Grassmann matrix pairs with arbitrary permutation from a new perspective. The new explicit expressions of the chordal metric between generalized singular values of Grassmann matrix pairs with arbitrary permutation are presented, which result in only two small-size singular value decompositions to evaluate. The proposed results are generalizations of several results on bounds on perturbation of generalized singular values.

  • Keywords

Perturbation analysis, Chordal metric, Generalized singular value, Grassman matrix pair, Arbitrary permutation.

  • AMS Subject Headings

15A18, 15A23, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JICS-19-15, author = {Wang , YujieZhu , Lei and Xu , Weiwei}, title = {New Perturbation Analysis of Generalized Singular Values of Grassmann Matrix Pairs with Arbitrary Permutation}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {19}, number = {1}, pages = {15--40}, abstract = {

In this paper we give new perturbation analysis of generalized singular values of Grassmann matrix pairs with arbitrary permutation from a new perspective. The new explicit expressions of the chordal metric between generalized singular values of Grassmann matrix pairs with arbitrary permutation are presented, which result in only two small-size singular value decompositions to evaluate. The proposed results are generalizations of several results on bounds on perturbation of generalized singular values.

}, issn = {3080-180X}, doi = {https://doi.org/10.4208/JICS-2024-002}, url = {http://global-sci.org/intro/article_detail/jics/23877.html} }
TY - JOUR T1 - New Perturbation Analysis of Generalized Singular Values of Grassmann Matrix Pairs with Arbitrary Permutation AU - Wang , Yujie AU - Zhu , Lei AU - Xu , Weiwei JO - Journal of Information and Computing Science VL - 1 SP - 15 EP - 40 PY - 2024 DA - 2024/03 SN - 19 DO - http://doi.org/10.4208/JICS-2024-002 UR - https://global-sci.org/intro/article_detail/jics/23877.html KW - Perturbation analysis, Chordal metric, Generalized singular value, Grassman matrix pair, Arbitrary permutation. AB -

In this paper we give new perturbation analysis of generalized singular values of Grassmann matrix pairs with arbitrary permutation from a new perspective. The new explicit expressions of the chordal metric between generalized singular values of Grassmann matrix pairs with arbitrary permutation are presented, which result in only two small-size singular value decompositions to evaluate. The proposed results are generalizations of several results on bounds on perturbation of generalized singular values.

Wang , YujieZhu , Lei and Xu , Weiwei. (2024). New Perturbation Analysis of Generalized Singular Values of Grassmann Matrix Pairs with Arbitrary Permutation. Journal of Information and Computing Science. 19 (1). 15-40. doi:10.4208/JICS-2024-002
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