Inverse properties of a class of seven-diagonal (near) Toeplitz matrices-Reference-Cited by-同舟云学术

Inverse properties of a class of seven-diagonal (near) Toeplitz matrices

Published:2021-10-09 Issue:1 Volume:10 Page:67-86
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Kurmanbek Bakytzhan¹,Erlangga Yogi²,Amanbek Yerlan¹

Affiliation:

1. Nazarbayev University , Department of Mathematics , 53 Kabanbay Batyr Ave, Nur-Sultan 010000 , Kazakhstan

2. Zayed University , Department of Mathematics , Abu Dhabi Campus, P.O. Box 144534 , United Arab Emirates

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2021-0148/pdf

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