# MathSciDoc: An Archive for Mathematician ∫

#### Numerical Analysis and Scientific Computingmathscidoc:1609.25011

2016.5
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.
Nonlinear matrix equation,Sherman Morrison Woodbury formula,Maximal positive definite solution,Flow,Positive operator,Doubling algorithm, R-superlinear with order $r$
@inproceedings{chun-yueh,2016on,
title={On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$},

Chun-Yueh, Chiang. On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902132058935221610.