Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants

@article{Brent1980FastSO,
title={Fast Solution of Toeplitz Systems of Equations and Computation of Pad{\'e} Approximants},
author={Richard P. Brent and Fred G. Gustavson and David Y. Y. Yun},
journal={J. Algorithms},
year={1980},
volume={1},
pages={259-295}
}

We present two new algorithms, ADT and MDT, for solving order-n Toeplitz systems of linear equations Tz = b in time O(n log n) and space O(n). The fastest algorithms previously known, such as Trench’s algorithm, require time Ω(n2) and require that all principal submatrices of T be nonsingular. Our algorithm ADT requires only that T be nonsingular. Both our algorithms for Toeplitz systems are derived from algorithms for computing entries in the Padé table for a given power series. We prove that… CONTINUE READING