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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations and , 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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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