Parallel multi-splitting methods for nonlinear quadratic matrix equation

摘要

In this paper, motivated by multi-splitting methods, a nonlinear method for solving the quadratic matrix equation (QME) is constructed. Meanwhile, nonlinear multi-splitting algorithm and nonlinear multi-splitting Newton algorithm are presented to find the solution to QME. Then under suitable conditions, the local linear and quadratic convergence of the algorithms are proved respectively. In the end, a numerical result is given to show the feasibility and effectiveness of these algorithms.