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An algorithm for computing positive definite solutions of the nonlinear matrix equation X + A*X-1A = I
Author:
Salah M. El-Sayed a
| Affiliation: | a Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt |
DOI:
10.1080/00207160310001603316
Publication Frequency:
15 issues per year
Published in:
International Journal of Computer Mathematics,
Volume
80,
Issue
12
December
2003
, pages 1527
- 1534
International Journal of Computer Mathematics,
Volume
80,
Issue
12
December
2003
, pages 1527
- 1534
Subjects:
Analysis - Mathematics;
Bioinformatics;
Computer Mathematics;
Discrete Mathematics;
Mathematical Finance;
Mathematical Logic;
Mathematical Numerical Analysis;
Systems & Computer Architecture;
Number of References: 14
Formats available:
PDF
(English)
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Abstract
In this paper, an algorithm for obtaining the Hermitian positive definite solutions of the nonlinear matrix equation X + A*X-1A = I is considered and discussed. The convergence of the algorithm is proved. Numerical experiments to illustrate the behavior of the algorithm are executed.
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| Keywords: Nonlinear matrix equation; Iteration methods; Convergence of sequences; Positive definite matrix |
| view references (14) |
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