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

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초록

We consider the nonlinear matrix equation Xp + AXqB +CXD + E = 0, where p and q are positive integers, A;B and E are n nnonnegative matrices, C and D are arbitrary n n real matrices. A su -cient condition for the existence of the elementwise minimal nonnegativesolution is derived. The monotone convergence of Newton's method forsolving the equation is considered. Several numerical examples to showthe e ciency of the proposed Newton's method are presented.

Abstract

We consider the nonlinear matrix equation Xp + AXqB +CXD + E = 0, where p and q are positive integers, A;B and E are n nnonnegative matrices, C and D are arbitrary n n real matrices. A su -cient condition for the existence of the elementwise minimal nonnegativesolution is derived. The monotone convergence of Newton's method forsolving the equation is considered. Several numerical examples to showthe e ciency of the proposed Newton's method are presented.

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