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

  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},
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
Highly Influential
This paper has highly influenced 18 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
187 Citations
1 References
Similar Papers


Publications referenced by this paper.

Fast solution of Toeplitz systems of equations and computation of Padé approximants

  • R. P. Brent, F. G. Gustavson, D.Y.Y. Yun
  • J. Algorithms
  • 1980
1 Excerpt

Similar Papers

Loading similar papers…