Fast inversion of triangular Toeplitz matrices

Authors:
Fu-Rong Lin;Wai-Ki Ching;Michael K. Ng
Affiliations:
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, PR China and Department of Mathematics, the University of Hong Kong, Pokfulam road, Hong Kong;Department of Mathematics, the University of Hong Kong, Pokfulam road, Hong Kong;Department of Mathematics, the University of Hong Kong, Pokfulam road, Hong Kong
Venue:
Theoretical Computer Science - Algebraic and numerical algorithm
Year:
2004

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Abstract

In this paper, we present an approximate inversion method for triangular Toeplitz matrices based on trigonometric polynomial interpolation. To obtain an approximate inverse of high accuracy for a triangular Toeplitz matrix of size n, our algorithm requires two fast Fourier transforms (FFTs) and one fast cosine transform of 2n-vectors. We then revise the approximate method proposed by Bini (SIAM J. Comput. 13 (1984) 268). The complexity of the revised Bini algorithm is two FFTs of 2n-vectors.