一种求解加权Toeplitz最小二乘问题的新预条件子（英文）

A New Preconditioner for Solving Weighted Toeplitz Least Squares Problems

本文研究加权Toeplitz最小二乘问题的快速求解算法.首先,在增广线性系统的基础上,设计了一种用于求解此类线性系统的新型简单预条件子.其次,研究了迭代法的收敛性,并证明了预条件矩阵的所有特征值均是实数且非单位特征值位于某正区间.再次,研究了预条件矩阵的特征向量分布和最小多项式的维数.最后,相关数值实验表明新型预条件子比一些已有的预条件子更有效.

In this paper,we study a fast algorithm for solving the weighted Toeplitz least squares problems.Firstly,on the basis of the augmented linear system,we develop a new SIMPLE-like Preconditioner for solving such linear systems.Secondly,the convergence of the iterative method is studied,and used to prove that all eigenvalues of the preconditioned matrix are real and nonunit eigenvalues are located in a positive interval.Again,we also study the eigenvector distribution and the degree of the minimal polynomial of the preconditioned matrix.Finally,related numerical experiments are carried out to show that the new preconditioner is more effective than some existing preconditioners.