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Iterative solution of two matrix equations


Authors: Chun-Hua Guo and Peter Lancaster
Journal: Math. Comp. 68 (1999), 1589-1603
MSC (1991): Primary 15A24, 65F10; Secondary 65H10, 93B40
DOI: https://doi.org/10.1090/S0025-5718-99-01122-9
Published electronically: April 7, 1999
MathSciNet review: 1651757
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Abstract: We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$, where $Q$ is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation. Numerical results are reported to illustrate the convergence behaviour of various algorithms.


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Additional Information

Chun-Hua Guo
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Address at time of publication: Department of Computer Science, University of California, Davis, California 95616-8562
Email: guo@cs.ucdavis.edu

Peter Lancaster
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email: lancaste@ucalgary.ca

DOI: https://doi.org/10.1090/S0025-5718-99-01122-9
Keywords: Matrix equations, positive definite solution, fixed point iteration, Newton's method, convergence rate, matrix pencils
Received by editor(s): January 22, 1998
Published electronically: April 7, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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