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

摘要

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 dierential equation with anite dierence method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the xed-point iteration used to solve the dierential 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.