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

Kurmanbek B. Erlangga Y. Amanbek Y.
1 January 2022 De Gruyter Open Ltd

Special Matrices
2022 #10 Issue 1

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.

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

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Nazarbayev University, Department of Mathematics, 53 Kabanbay Batyr Ave, Nur-Sultan, 010000, Kazakhstan
Zayed University, Department of Mathematics, Abu Dhabi Campus, P.O. Box 144534, United Arab Emirates
Nazarbayev University, Department of Mathematics, 53 Kabanbay Batyr Ave, Nur-Sultan, 010000, Kazakhstan

Nazarbayev University
Zayed University
Nazarbayev University

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