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J. Korean Math. Soc. 2018; 55(2): 327-342
Online first article February 5, 2018 Printed March 1, 2018
https://doi.org/10.4134/JKMS.j170202
Copyright © The Korean Mathematical Society.
A homotopy continuation method for solving a matrix equation
Jing Li, Yuhai Zhang
Shandong University, Shandong University
In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-\sum_{i=1}^{m}A_{i}^*X^{-p_{i}}A_{i}=I$ with $p_{i}> 1$ is proposed, which does not depend on a good initial approximation to the solution of matrix equation.
Keywords: nonlinear matrix equation, Hermitian positive definite solution, homotopy continuation method, Kronecker product
MSC numbers: 15A24, 15A48
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