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Volume 25, Issue 5
On the Rayleigh Quotient for Singular Values

Xiaoshan Chen & Wen Li

J. Comp. Math., 25 (2007), pp. 512-521.

Published online: 2007-10

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  • Abstract

In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, and some results of the Rayleigh quotient (matrix) of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.

  • Keywords

The singular value, Rayleigh quotient, Canonical angle matrix.

  • AMS Subject Headings

65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-512, author = {Xiaoshan Chen and Wen Li}, title = {On the Rayleigh Quotient for Singular Values}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {512--521}, abstract = {

In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, and some results of the Rayleigh quotient (matrix) of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8709.html} }
TY - JOUR T1 - On the Rayleigh Quotient for Singular Values AU - Xiaoshan Chen & Wen Li JO - Journal of Computational Mathematics VL - 5 SP - 512 EP - 521 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8709.html KW - The singular value, Rayleigh quotient, Canonical angle matrix. AB -

In this paper, the theoretical analysis for the Rayleigh quotient matrix is studied, and some results of the Rayleigh quotient (matrix) of Hermitian matrices are extended to those for arbitrary matrix on one hand. On the other hand, some unitarily invariant norm bounds for singular values are presented for Rayleigh quotient matrices. Our results improve the existing bounds.

Xiaoshan Chen and Wen Li. (2007). On the Rayleigh Quotient for Singular Values. Journal of Computational Mathematics. 25 (5). 512-521. doi:
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