求解Toeplitz线性系统的一种新的分裂迭代法

A New Splitting for Iteratively Solving Toeplitz Systems

对于Toeplitz线性系统,借助于其特殊结构,文章提出了一种新的分裂迭代法,即将Toeplitz矩阵分裂为一个循环矩阵和另一矩阵之和.理论分析表明,在一定的条件下,该方法收敛于Toeplitz线性系统的唯一解.数值实验表明新的方法是有效的.

For Toeplitz linear systems,by using its special structure,in this paper,we pro- pose a new splitting iterative method,which divides the Toeplitz matrix into a sum of a circulant matrix and an arbitrary matrix. Theoretical analysis shows that the new method converges under reasonable conditions to the unique solution of the Toeplitz linear system. Numerical experiments further show that the new method is effective.