Article
Inverse properties of a class of seven-diagonal (near) Toeplitz matrices
Special Matrices
Document Type
Article
Publication Date
10-9-2021
Abstract
This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.
DOI Link
Publisher
De Gruyter
Disciplines
Keywords
- Seven-diagonal matrices,
- Toeplitz,
- Exact inverse,
- Upper bound of norm of inverse
Scopus ID
Creative Commons License
Creative Commons Attribution 4.0 International
Indexed in Scopus
Yes
Open Access
Yes
Open Access Type
Gold: This publication is openly available in an open access journal/series
Citation Information
Bakytzhan Kurmanbek, Yogi Erlangga and Yerlan Amanbek. "Inverse properties of a class of seven-diagonal (near) Toeplitz matrices" Special Matrices Vol. 10 Iss. 1 (2021) p. 67 - 86 ISSN: <p><a href="https://v2.sherpa.ac.uk/id/publication/issn/2300-7451" target="_blank">2300-7451</a></p> Available at: http://works.bepress.com/yogi-erlangga/5/