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

Chun-Yueh, Chiang Center for General Education, National Formosa University, Huwei 632, Taiwan.

Numerical Analysis and Scientific Computing mathscidoc: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 $r$
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@inproceedings{chun-yueh,2016on,
  title={On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$},
  author={Chun-Yueh, Chiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160902132058935221610},
  year={2016},
}
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.
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