Mathematics of Computation

Author(s): Chun-Hua Guo; Peter Lancaster.
Journal: Math. Comp. 68 (1999), 1589-1603.
MSC (1991): Primary 15A24, 65F10; Secondary 65H10, 93B40
Posted: April 7, 1999
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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

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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Retrieve articles in Mathematics of Computation with MSC (1991): 15A24, 65F10, 65H10, 93B40

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: 10.1090/S0025-5718-99-01122-9
PII: S 0025-5718(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
Posted: April 7, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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