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A note on the fixed-point iteration for the matrix equations X±A∗X-1A=I

Published:2008-10 Issue:8-9 Volume:429 Page:2098-2112
ISSN:0024-3795
Container-title:Linear Algebra and its Applications
language:en
Short-container-title:Linear Algebra and its Applications

Author:

Fital Sandra,Guo Chun-Hua

Publisher

Elsevier BV

Subject

Discrete Mathematics and Combinatorics,Geometry and Topology,Numerical Analysis,Algebra and Number Theory

Reference18 articles.

1. Positive solutions to X=A-BX-1B∗;Anderson;Linear Algebra Appl.,1990

2. P. Benner, H. Fassbender, On the solution of the rational matrix equation X=Q+LX-1LT, EURASIP J. Adv. Signal Process. 2007, 10 (Art. ID 21850).

3. C.-Y. Chiang, E.K.-W. Chu, C.-H. Guo, T.-M. Huang, W.-W. Lin, S.-F. Xu, Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case, Preprint, 2008.

4. On the existence of a positive definite solution of the matrix equation X+ATX-1A=I;Engwerda;Linear Algebra Appl.,1993

5. Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X+A∗X-1A=Q;Engwerda;Linear Algebra Appl.,1993

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