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A pivoting strategy for symmetric tridiagonal matrices
Author(s) -
Bunch James R.,
Marcia Roummel F.
Publication year - 2005
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.432
Subject(s) - tridiagonal matrix , mathematics , tridiagonal matrix algorithm , triangular matrix , matrix (chemical analysis) , block (permutation group theory) , combinatorics , block matrix , factorization , a priori and a posteriori , upper and lower bounds , lu decomposition , matrix decomposition , algorithm , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , philosophy , physics , materials science , epistemology , composite material , quantum mechanics , invertible matrix
The LBL T factorization of Bunch for solving linear systems involving a symmetric indefinite tridiagonal matrix T is a stable, efficient method. It computes a unit lower triangular matrix L and a block 1 × 1 and 2 × 2 matrix B such that T = LBL T . Choosing the pivot size requires knowing a priori the largest element σ of T in magnitude. In some applications, it is required to factor T as it is formed without necessarily knowing σ. In this paper, we present a modification of the Bunch algorithm that can satisfy this requirement. We demonstrate that this modification exhibits the same bound on the growth factor as the Bunch algorithm and is likewise normwise backward stable. Copyright © 2005 John Wiley & Sons, Ltd.