Source of Publication
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.
Physical Sciences and Mathematics
Seven-diagonal matrices, Toeplitz, Exact inverse, Upper bound of norm of inverse
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Kurmanbek, Bakytzhan; Erlangga, Yogi; and Amanbek, Yerlan, "Inverse properties of a class of seven-diagonal (near) Toeplitz matrices" (2021). All Works. 4619.
Indexed in Scopus
Open Access Type
Gold: This publication is openly available in an open access journal/series