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

“This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, whicharises in the numerical solutions of nonlinear fourth-order dierential equation with a nite dierencemethod. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Relatedto the xed-point iteration used to solve the dierential equation, we show the positivity of the inverse matrixand construct an upper bound for the norms of the inverse matrix, which can be used to predict the conver-gence of the method.”