矩阵方程AXB=C的最佳逼近对称解的迭代算法

Iterative algorithms for the best approximation to symmetric solutions of the matrix equation AXB=C

摘要: 基于求解线性方程组Mx=f的思想，给出了求解矩阵方程AXB=C最佳逼近对称解的Douglas Rachford分裂算法、Dykstra’s交替投影算法以及LSQR算法的具体计算方法，得到了基于LSQR算法的解的表达式。最后通过数值实验比较了不同矩阵规模下3种算法求解矩阵方程AXB=C最佳逼近对称解的迭代时间，并分析了算法的收敛特性。

Abstract: Based on the ideas of solving linear equations Mx=f, the Douglas Rachford splitting algorithm, Dykstra´s alternating projection algorithm and LSQR algorithm for solving the optimal approximate symmetric solution of matrix equation AXB=C is given, and the expression of the solution based on LSQR algorithm is obtained. Finally, the iterative time of three algorithms for solving the optimal approximate symmetric solution of matrix equation AXB=C under different matrix sizes is compared by numerical experiments, and the convergence characteristics of the algorithm are analyzed.