On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$
Numerical Analysis
2016-10-13 v7
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 is then designed to solve the maximal positive definite solution efficiently.
Keywords
Cite
@article{arxiv.1602.02199,
title = {On a class of nonlinear matrix equations $X\pm A^{\small H}f(X)^{-1}A=Q$},
author = {Chun-Yueh Chiang},
journal= {arXiv preprint arXiv:1602.02199},
year = {2016}
}