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http://dx.doi.org/10.12941/jksiam.2010.14.2.113

SOLVING A MATRIX POLYNOMIAL BY NEWTON'S METHOD  

Han, Yin-Huan (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
Kim, Hyun-Min (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.14, no.2, 2010 , pp. 113-124 More about this Journal
Abstract
We consider matrix polynomial which has the form $P_1(X)=A_oX^m+A_1X^{m-1}+...+A_m=0$ where X and $A_i$ are $n{\times}n$ matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation $P_1(X)$. Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton's method. Finally, we give some numerical experiments that confirm the theoretical results.
Keywords
matrix polynomial; solvent; Newton's method; iterative method; symmetric and generalized centro-symmetric;
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Times Cited By KSCI : 2  (Citation Analysis)
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