研究由Nash均衡对策导出的一类双矩阵变量Riccati矩阵方程 (R-ME)异类约束解的数值计算问题.运用牛顿算法将R-ME的异类约束解问题转化为双矩阵变量线性矩阵方程的异类约束解或者异类约束最小二乘解问题,采用修正共轭梯度法解决后一问题,可建立求R-ME的异类约束解的新型迭代算法.数值算例表明,新型迭代算法是有效的.

In this paper, a new iterative method is studied to find different constrained solutions of a kind of two-variable Riccati matrix equation which associated with the Nash equilibrium strategies. At the first place, we apply Newton's method to the R-ME for computing  the different constrained solutions, then a problem to find different  constrained solutions or different constrained least-square solutions   of a linear matrix equation will be derived. Moreover, we use the modified
  conjugate gradient method to solve the derived linear matrix equation. Finally, a new iterative method is established to find different constrained solutions of the R-ME. Numerical examples show that the new iterative method is effective.