Year: 1991
Author: Ji-Guang Sun
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 3 : pp. 247–255
Abstract
Let {$A,B$} be a definite matrix pair of order $n$, and let $Z$ be an $l$-dimensional subspace of $C^n$. In this paper we introduce the Rayleigh quotient matrix pair
{$H_1,K_1$} and residual matrix pair {$R_A,R_B$} of {A,B} with respect to Z, and used the norm of {$R_A,R_B$} to bound the difference between the eigenvalues of {$H_1,K_1$} and that of {$A,B$}, and to bound the difference between $Z$ and an $l$-dimensional eigenspace of {$A,B$}. The corresponding classical theorems on the Hermitian matrices can be derived from the results of this paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1991-JCM-9398
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 3 : pp. 247–255
Published online: 1991-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9