A note on computing the inverse of a triangular Toeplitz matrix

Abstract

Using trigonometric polynomial interpolation, a fast and effective numerical algorithm for computing the inverse of a triangular Toeplitz matrix with real numbers has been recently proposed (Lin et al., 2004) [7]. The complexity of the algorithm is two fast Fourier transforms (FFTs) and one fast cosine transform (DCT) of 2n-vectors. In this paper, we present an algorithm with two fast Fourier transforms (FFTs) of 2n-vectors for calculating the inverse of a triangular Toeplitz matrix with real and/or complex numbers. A theoretical accuracy and error analysis is also considered. Numerical examples are given to illustrate the effectiveness of our method.