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On the Solution of the Rational Matrix Equation

EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 021850 (2007) Cite this article

Abstract

We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation, where is symmetric positive definite and is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE). We discuss how to use the butterfly algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, 09107, Germany

    Peter Benner

  2. Institut Computational Mathematics, Technische Universität Braunschweig, Braunschweig, 38106, Germany

    Heike Faßbender

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  1. Peter Benner
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  2. Heike Faßbender
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Correspondence to Peter Benner.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Benner, P., Faßbender, H. On the Solution of the Rational Matrix Equation. EURASIP J. Adv. Signal Process. 2007, 021850 (2007). https://doi.org/10.1155/2007/21850

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  • DOI: https://doi.org/10.1155/2007/21850

Keywords

  • Information Technology
  • Iterative Method
  • Quantum Information
  • Matrix Equation
  • Riccati Equation