CONDITION AND ACCURACY OF ALGORITHMS FOR COMPUTING SCHUR COEFFICIENTSOF TOEPLITZ MATRICES

Authors
GOHBERG I KOLTRACHT I XIAO D
Citation
I. Gohberg et al., CONDITION AND ACCURACY OF ALGORITHMS FOR COMPUTING SCHUR COEFFICIENTSOF TOEPLITZ MATRICES, SIAM journal on matrix analysis and applications, 15(4), 1994, pp. 1290-1309
Citations number
21
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on matrix analysis and applications → ACNP
ISSN journal
08954798
Volume
15
Issue
4
Year of publication
1994
Pages
1290 - 1309
Database
ISI
SICI code
0895-4798(1994)15:4<1290:CAAOAF>2.0.ZU;2-G
Abstract
A formula for the condition number of Schur coefficients of a positive definite Toeplitz matrix is obtained and an efficient algorithm for c omputing the condition number is given. New bounds of backward roundof f errors in Schur and Levinson algorithms for computing Schur coeffici ents are presented. These bounds, together.with the condition number, provide a posteriori estimate of the error in computed Schur coefficie nts. Numerical comparison of Schur and Levinson algorithms with the LD L(T) algorithm also indicates their forward stability.