Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure

@inproceedings{Gohberg2010FastGE,
  title={Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure},
  author={Israel Gohberg and Thomas Kailath and Vadim Olshevsky},
  year={2010}
}
Fast 0(n2) implementation of Gaussian elimination with partial pivoting is designed for matrices possessing Cauchy-like displacement structure. We show how Toeplitz-like, Toeplitz-plus-Hankel-like and Vandermondelike matrices can be transformed into Cauchy-like matrices by using Discrete Fourier, Cosine or Sine Transform matrices. In particular this allows us to propose a new fast 0{n2) Toeplitz solver GKO, which incorporates partial pivoting. A large set of numerical examples showed that GKO… CONTINUE READING
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