Rayleigh Quotient and Residual of a Definite Pair
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 Cn. In this paper we introduce the Rayleigh quotient matrix pair
{H1,K1} and residual matrix pair {RA,RB} of {A,B} with respect to Z, and used the norm of {RA,RB} to bound the difference between the eigenvalues of {H1,K1} 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
Author Details
Ji-Guang Sun Email