Record Details

Finite-rank methods and their stability for coupled systems of operator equations

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title Finite-rank methods and their stability for coupled systems of operator equations
 
Creator LARGILLIER, A
LIMAYE, BV
 
Subject finite-rank operator
sylvester equation
spectrum
(semisimple) eigenvalue
iterative refinement scheme
stability of a solution
condition number
 
Description Let K be a bounded linear operator of finite rank on a normed linear space X. The solution of a coupled system of linear equations involving K is reduced to a solution of a matrix Sylvester equation L - K = . It is shown that this equation has a unique solution satisfying P-sigma = (0) under bar (resp., V-S = (0) under bar), provided P-sigma = (0) under bar (resp., V-S = (0) under bar) where P-sigma and V-S are certain projections related to the spectra sigma(K) and sigma(L) of K and L, resp. The stability of such a solution of a matrix Sylvester equation is considered and is related to the stability of a similar solution of the coupled system involving the operator K. Often K is an approximation of a bounded linear operator F on X, yielding an approximate computable solution of either a coupled system involving F or of an eigenvalue problem for F. Iterative refinement of such a computed solution can be accomplished by solving suitable matrix Sylvester equations. Numerical examples are given to illustrate this procedure.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T05:01:04Z
2011-12-26T12:58:25Z
2011-12-27T05:48:18Z
2011-08-29T05:01:04Z
2011-12-26T12:58:25Z
2011-12-27T05:48:18Z
1996
 
Type Article
 
Identifier SIAM JOURNAL ON NUMERICAL ANALYSIS, 33(2), 707-728
0036-1429
http://dx.doi.org/10.1137/0733036
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11967
http://hdl.handle.net/10054/11967
 
Language en