Double Iterative Algorithm for Symmetric Solution of Multi-variable Quadratic Matrix Equation

In this article, a double iterative methods is suggested for solving symmetric matrix of multi-variable quadratic matrix equation. Firstly, the symmetric matrix of a quadratic matrix equation is transformed into the symmetric matrix of the corrected matrix equation by the Newton's algorithm. Then, we develop a modified conjugate gradient algorithm (MCG) for finding a symmetric solution of the modified equation. A numerical example is offered to show the inefficiency of the double iterative methods.