求解广义复Sylvester张量方程的子空间迭代法

The Subspace Iteration Method for Solving Generalized Complex Sylvester Tensor Equations

本文研究求解广义复Sylvester张量方程的修正共轭梯度法(MCG)和共轭梯度最小二乘法(CGLS).它们都基于求解线性方程组的经典Krylov子空间方法.在不计舍入误差的情况下,理论分析表明对于任意初始张量,所提出的算法收敛到Sylvester张量方程的解.数值结果验证了MCG算法和CGLS算法的有效性.

In this paper,the modified conjugate gradient(MCG)method and the conjugate gradient least squares(CGLS)method are proposed to solve the generalized complex Sylvester tensor equations.They are all based on the classical Krylov subspace method for solving linear equations.Theoretical analysis shows that the proposed algorithm converges to Sylvester tensor equation solutions for any initial tensors,excluding rounding errors.The numerical results show that the MCG algorithm and CGLS algorithm are effective.