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Stability properties of superoptimal preconditioner from numerical range
Author(s) -
Cheng CheMan,
Jin XiaoQing,
Wei YiMin
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.472
Subject(s) - preconditioner , mathematics , eigenvalues and eigenvectors , matrix (chemical analysis) , stability (learning theory) , numerical range , complex matrix , pure mathematics , mathematical analysis , chemistry , linear system , computer science , physics , chromatography , quantum mechanics , machine learning
A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix A n , we give some sufficient and necessary conditions for the stability of superoptimal preconditioner E U ( A n ) proposed by Tyrtyshnikov ( SIAM J. Matrix Anal. Appl. 1992; 13 :459–473). Copyright © 2005 John Wiley & Sons, Ltd.