Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A HOMOTOPY CONTINUATION METHOD FOR SOLVING A MATRIX EQUATION

  • Li, Jing (School of Mathematics Shandong University) ;
  • Zhang, Yuhai (School of Mathematics Shandong University)
  • Received : 2017.03.21
  • Accepted : 2017.11.30
  • Published : 2018.03.01
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Abstract

In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-{\sum_{i=1}^{m}}A^{\ast}_iX^{-p_i}A_i=I$ with $p_i$ > 1 is proposed, which does not depend on a good initial approximation to the solution of matrix equation.

Keywords

Acknowledgement

Supported by : National Nature Science Foundation of China

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