最速下降法解二次矩阵方程

The Steepest Descent Method for the Quadratic Matrix Equation

分析了牛顿法解二次方程的优点和缺点.结合优化理论中最速下降法思想,给出一种新的算法解二次矩阵方程,并列出几个数值例子说明算法是可行的.

The merit and defect of Newton method for the quadratic matrix equation were analyzed. The steepest descent method was applied in optimization to solve the quadratic matrix equation, and a new algorithm was given. Several numerical examples were presented to illustrate the feasibility of our algorithm