Inversion of Toeplitz Band Matrices

An algorithm for inverting Toeplitz matrices is simplified for Toeplitz band matrices. In some cases, the simplification yields formulas for the elements in the first row and column of the inverse, from which the remaining elements can be easily calculated. Two examples are given. In any case, the simplification yields a recursive method for computing the first row and column of the inverse of an nth order Toeplitz band matrix with $O(n)$ operations, where $O({n^2})$ are required with the more general algorithm.