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A homotopy continuation method for solving a matrix equation

Jing Li|Yuhai Zhang
대한수학회 (The Korean Mathematical Society)|2018.03|대한수학회지 (Journal of the KMS)|제55권 제2호|pp. 327-342

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참고문헌

키워드

Kronecker productnonlinear matrix equationHermitian positive definite solutionhomotopy continuation method
주제분류수학

초록

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.

Abstract

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

참고문헌 (20)

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