THE GENERALIZED SCHUR DECOMPOSITION OF AN ARBITRARY PENCIL-A - LAMBDA-B - ROBUST SOFTWARE WITH ERROR-BOUNDS AND APPLICATIONS .1. THEORY ANDALGORITHMS

Citation
J. Demmel et B. Kagstrom, THE GENERALIZED SCHUR DECOMPOSITION OF AN ARBITRARY PENCIL-A - LAMBDA-B - ROBUST SOFTWARE WITH ERROR-BOUNDS AND APPLICATIONS .1. THEORY ANDALGORITHMS, ACM transactions on mathematical software, 19(2), 1993, pp. 160-174
Citations number
46
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Sciences",Mathematics
ISSN journal
0098-3500
Volume
19
Issue
2
Year of publication
1993
Pages
160 - 174
Database
ISI
SICI code
0098-3500(1993)19:2<160:TGSDOA>2.0.ZU;2-0
Abstract
Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A - lambdaB (regular or si ngular) is presented. The decomposition is a generalization of the Sch ur canonical form of A - lambdaI to matrix pencils and reveals the Kro necker structure of a singular pencil. Since computing the Kronecker s tructure of a singular pencil is a potentially ill-posed problem, it i s important to be able to compute rigorous and reliable error bounds f or the computed features. The error bounds rely on perturbation theory for reducing subspaces and generalized eigenvalues of singular matrix pencils. The first part of this two-part paper presents the theory an d algorithms for the decomposition and its error bounds, while the sec ond part describes the computed generalized Schur decomposition and th e software, and presents applications and an example of its use.