NEWTON'S METHOD FOR SYMMETRIC AND BISYMMETRIC SOLVENTS OF THE NONLINEAR MATRIX EQUATIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 50, Issue 4, 2013, pp.755-770
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2013.50.4.755

Title & Authors

NEWTON'S METHOD FOR SYMMETRIC AND BISYMMETRIC SOLVENTS OF THE NONLINEAR MATRIX EQUATIONS

Han, Yin-Huan; Kim, Hyun-Min;

Han, Yin-Huan; Kim, Hyun-Min;

Abstract

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by , where X is a unknown real matrix, and A, B and C are given matrices with real elements. Another one is the matrix polynomial . Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Frchet derivative. Finally, we give some numerical examples.

Keywords

quadratic matrix equation;matrix polynomial;solvent;Newton's method;iterative algorithm;symmetric;bisymmetric;

Language

English

Cited by

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