Rayleigh Quotient and Residual of a Definite Pair

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 $C^n$. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Keywords:   

Author Details

Ji-Guang Sun