### CONVERGENCE OF NEWTON'S METHOD FOR SOLVING A NONLINEAR MATRIX EQUATION

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Meng, Jie;Lee, Hyun-Jung;Kim, Hyun-Min

• 투고 : 2015.11.05
• 심사 : 2016.01.02
• 발행 : 2016.01.30
• 6 13

#### 초록

We consider the nonlinear matrix equation $X^p+AX^qB+CXD+E=0$, where p and q are positive integers, A, B and E are $n{\times}n$ nonnegative matrices, C and D are arbitrary $n{\times}n$ real matrices. A sufficient condition for the existence of the elementwise minimal nonnegative solution is derived. The monotone convergence of Newton's method for solving the equation is considered. Several numerical examples to show the efficiency of the proposed Newton's method are presented.

#### 키워드

Matrix equation;Elementwise nonnegative solution;Newton's method;M-matrix

#### 참고문헌

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