Document Type
Article
Source of Publication
Special Matrices
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
ISSN
Publisher
De Gruyter
Volume
10
Issue
1
First Page
67
Last Page
86
Disciplines
Physical Sciences and Mathematics
Keywords
Seven-diagonal matrices, Toeplitz, Exact inverse, Upper bound of norm of inverse
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Kurmanbek, Bakytzhan; Erlangga, Yogi; and Amanbek, Yerlan, "Inverse properties of a class of seven-diagonal (near) Toeplitz matrices" (2021). All Works. 4619.
https://zuscholars.zu.ac.ae/works/4619
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series