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
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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
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