求AXB=C的对称反自反矩阵解及其最佳逼近的迭代解法

Iterative Method for the Symmetric Anti-reflexive Matrix Solutions and the Optimal Approximation of the Matrix Equation

采用迭代法讨论了矩阵方程的对称反自反矩阵解及其最佳逼近问题.证明了(i)若问题Ⅰ有解,则可在有限步求出一个迭代解,(ii)若取特殊初始矩阵,则可迭代出问题Ⅰ的极小范数解;并给出了最佳逼近问题的极小范数解.

This paper discusses related iterative method for the symmetric anti -reflexive solutions and the optimal approximation of. Proof that （i） when Problem I is solvable, its solution can be obtained within finite iterative steps,（ii） when set the special initial matrix, then its leastnorm solution can be obtained within finite steps. Furthermore, the least - norm solution of the optimal approximation is given.