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

Bakytzhan Kurmanbek; Yogi Erlangga; Yerlan Amanbek

doi:10.1515/spma-2021-0148

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

Bakytzhan Kurmanbek, Yogi Erlangga, Yerlan Amanbek

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Journal	Special Matrices
Volume	10
Issue number	1
DOIs	https://doi.org/10.1515/spma-2021-0148
Publication status	Published - Jan 1 2022

Keywords

exact inverse
seven-diagonal matrices
Toeplitz
upper bound of norm of inverse

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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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. ",

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AU - Amanbek, Yerlan

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N2 - 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.

AB - 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.

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KW - seven-diagonal matrices

KW - Toeplitz

KW - upper bound of norm of inverse

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

Abstract

Keywords

ASJC Scopus subject areas

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