A new algorithm for 5-band Toeplitz matrix inversion with application to GCV smoothing spline computation

Abstract

A new algorithm is developed for computing any entry of the inverse of a 5-band Toeplitz matrix. After a linear-time overhead, each entry can be computed in constant time. As an application of this algorithm, we present a way to compute the generalized cross validated smoothing spline in linear time for the equally spaced data case. (C) 1999 Elsevier Science B.V. All rights reserved.