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Article · Special Matrices · October 9, 2021
Inverse properties of a class of seven-diagonal (near) Toeplitz matrices
Bakytzhan Kurmanbek, Yogi A. Erlangga, Yerlan Amanbek
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.
Matrix Theory and AlgorithmsAdvanced Combinatorial MathematicsNumerical methods in inverse problemsSherman-Morrison formulafinite difference methodfixed point iteration
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