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http://dx.doi.org/10.4134/JKMS.j170202

A HOMOTOPY CONTINUATION METHOD FOR SOLVING A MATRIX EQUATION  

Li, Jing (School of Mathematics Shandong University)
Zhang, Yuhai (School of Mathematics Shandong University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 327-342 More about this Journal
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
nonlinear matrix equation; Hermitian positive definite solution; homotopy continuation method; Kronecker product;
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