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General resolution of a convergence question of L. Krukier
Author(s) -
Johnson Charles,
Krukier Lev
Publication year - 2009
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.681
Subject(s) - mathematics , norm (philosophy) , resolution (logic) , convergence (economics) , combinatorics , matrix (chemical analysis) , discrete mathematics , computer science , chemistry , law , political science , chromatography , artificial intelligence , economics , economic growth
It was shown that there exists a matrix norm N such that N ( A −1 B )<1 if A, B ∈ M n (), 0∉ F ( A ), and g ( A, B )<1 where g ( A, B )=max| z |, z ∈ G ( A, B ),\documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray*}G(A,B) = \left\{\frac{x^{*}Bx}{x^{*}Ax}:x \in {\mathscr{C}}^{n},x^{*}x = 1\right\}\end{eqnarray*}\end{document}Copyright © 2009 John Wiley & Sons, Ltd.