Properties of the inverses of a set of band matrices
W. D. Hoskins, G. E. McMaster · Linear and Multilinear Algebra · 1977
Those regions where the elements of the inverse of a Toeplitz matrix of band width four and order nalternate in sign are determined. A similar result concerning the elements of the inverse of a commonly occurring symmetric positive definite Toeplitz matrix of band width five and order nis extended to cover the case when the first and last rows of the matrix are modified through a change in the boundary conditions of the associated application. A method for economically obtaining the infinity norm of the pent-diagonal symmetric positive definite Toeplitz matrix is then derived.