# 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)
• Accepted : 2010.06.03
• Published : 2010.06.25

#### 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.

#### Acknowledgement

Supported by : Pusan National University

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