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On the growth factor in Gaussian elimination for generalized Higham matrices
Author(s) -
George Alan,
Ikramov Khakim D.,
Kucherov Andrey B.
Publication year - 2002
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.258
Subject(s) - gaussian elimination , hermitian matrix , mathematics , positive definite matrix , matrix (chemical analysis) , gaussian , combinatorics , class (philosophy) , factor (programming language) , upper and lower bounds , pure mathematics , mathematical analysis , physics , computer science , chemistry , computational chemistry , eigenvalues and eigenvectors , chromatography , quantum mechanics , artificial intelligence , programming language
A Higham matrix is a complex symmetric matrix A = B + iC , where both B and C are real, symmetric and positive definite. We prove that, for such A , the growth factor in Gaussian elimination is less than 3. Moreover, a slightly larger bound $${3\sqrt{2}}$$ holds true for a broader class of complex matrices A = B + iC , where B and C are Hermitian and positive definite. Copyright © 2002 John Wiley & Sons, Ltd.
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