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arXiv · 1602.02199

On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$

Chun-Yueh Chiang
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Abstract

Nonlinear matrix equations are encountered in many applications of control and engineering problems. In this work, we establish a complete study for a class of nonlinear matrix equations. With the aid of Sherman Morrison Woodbury formula, we have shown that any equation in this class has the maximal positive definite solution under a certain condition. Furthermore, A thorough study of properties about this class of matrix equations is provided. An acceleration of iterative method with R-superlinear convergence with order $r>1$ is then designed to solve the maximal positive definite solution efficiently.

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Chun-Yueh Chiang. 2016-02-06. On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$. https://arxiv.org/abs/1602.02199

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