East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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CONVERGENCE OF NEWTON'S METHOD FOR SOLVING A NONLINEAR MATRIX EQUATION

  • Meng, Jie (Department of Mathematics, Pusan National University) ;
  • Lee, Hyun-Jung (Department of Mathematics, Pusan National University) ;
  • Kim, Hyun-Min (Department of Mathematics, Pusan National University)
  • Received : 2015.11.05
  • Accepted : 2016.01.02
  • Published : 2016.01.30
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Abstract

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.

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References

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