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A generalized Schur-type algorithm for the joint factorization of a structured matrix and its inverse

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Abstract

A Schur-type algorithm is presented for the simultaneous triangular factorization of a given (non-degenerate) structured matrix and its inverse. The algorithm takes the displacement generator of a Hermitian, strongly regular matrixR as an input, and computes the displacement generator of the inverse matrixR −1 as an output. From these generators we can directly deduce theLD −1 L * (lower-diagonal-upper) decomposition ofR, and theUD −1 U * (upper-diagonallower) decomposition ofR −1. The computational complexity of the algorithm isO(rn 2) operations, wheren andr denote the size and the displacement rank ofR, respectively. Moreover, this method is especially suited for parallel (systolic array) implementations: usingn processors the algorithm can be carried out inO(n) steps.

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Authors and Affiliations

  1. Stanford University, Stanford, USA

    T. Boros

  2. University of California Los Angeles, Los Angeles, USA

    A. H. Sayed

  3. Northeastern University, USA

    H. Lev-Ari

  4. Stanford University, Stanford, USA

    T. Kailath

Authors
  1. T. Boros
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  2. A. H. Sayed
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  3. H. Lev-Ari
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  4. T. Kailath
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Boros, T., Sayed, A.H., Lev-Ari, H. et al. A generalized Schur-type algorithm for the joint factorization of a structured matrix and its inverse. Calcolo 33, 131–145 (1996). https://doi.org/10.1007/BF02575713

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  • DOI: https://doi.org/10.1007/BF02575713

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