A note on the paper “A note on inversion of Toeplitz matrices” by X.-G. Lv and T.-Z. Huang

In this note, we revisit the result of the Toeplitz matrix inversion formula proposed by Lv and Huang (2007), then we give a new structured perturbation analysis, which is useful for testing the stability of practical algorithms. It has been shown that our new upper bound is much sharper than the on...

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Bibliographic Details
Published inApplied mathematics letters Vol. 155; p. 109116
Main Authors Feng, Ting-Ting, Gu, Xian-Ming
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2024
Subjects
Inversion formula
Stability
Structured backward error
Toeplitz matrix
Inversion formula
Stability
Toeplitz matrix
Structured backward error
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Summary:In this note, we revisit the result of the Toeplitz matrix inversion formula proposed by Lv and Huang (2007), then we give a new structured perturbation analysis, which is useful for testing the stability of practical algorithms. It has been shown that our new upper bound is much sharper than the one they have given, especially when the size of the Toeplitz matrix is very large. Numerical experiments illustrate the effectiveness of our theoretical results.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2024.109116