Matrix Equations and Structures: Efficient Solution of Special Discrete Algebraic Riccati Equations

Authors:
Beatrice Meini
Affiliations:
-
Venue:
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Year:
2000

Citing 8
Cited 1

Computing the Extremal Positive Definite Solutions of a Matrix Equation

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On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems

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Asymptotic Results on the Spectra of Block Toeplitz Preconditioned Matrices

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Newton's Method for Discrete Algebraic Riccati Equations when the Closed-Loop Matrix Has Eigenvalues on the Unit Circle

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Effective Methods for Solving Banded Toeplitz Systems

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Iterative solution of two matrix equations

Mathematics of Computation
Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results

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Asymptotic spectral distribution of Toeplitz-related matrices

Fast reliable algorithms for matrices with structure

Some algorithms for solving special tridiagonal block Toeplitz linear systems

Journal of Computational and Applied Mathematics

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Abstract

We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, that allows the computation of the maximal solutions of the matrix equations X + C* X-1 C = Q, X - C* X-1 C = Q, X + C* (R + B* X B)-1 C = Q. The algorithm is based on the cyclic reduction method.