TY - JOUR
T1 - Rayleigh Quotient and Residual of a Definite Pair
AU - Sun , Ji-Guang
JO - Journal of Computational Mathematics
VL - 3
SP - 247
EP - 255
PY - 1991
DA - 1991/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9398.html
KW - 
AB - <p style="text-align: justify;">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&nbsp;<br/>{$H_1,K_1$} and residual matrix pair&nbsp; {$R_A,R_B$} 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.</p>