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On the Solution of the Rational Matrix Equation


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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Correspondence to Peter Benner.

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Benner, P., Faßbender, H. On the Solution of the Rational Matrix Equation. EURASIP J. Adv. Signal Process. 2007, 021850 (2007).

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