| 一种求解加权Toeplitz最小二乘问题的新预条件子（英文） |
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| 引用本文： | 程 国,李继成.一种求解加权Toeplitz最小二乘问题的新预条件子（英文）[J].应用数学,2020,33(1):172-185. |
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| 作者姓名： | 程 国 李继成 |
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| 作者单位： | 1. 西安交通大学数学与统计学院, 陕西 西安 710049; 2. 商洛学院数学与计算机应用学院, 陕西 商洛 726000 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(11671318);Natural Science Research Program Project of Education Department of Shaanxi Provincial(17JK0240) |
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| 摘 要： | 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.
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| 关 键 词： | 最小二乘问题 加权Toeplitz矩阵 预条件子 埃尔米特和反埃尔米特分裂 |
A New Preconditioner for Solving Weighted Toeplitz Least Squares Problems |
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| CHENG Guo,LI Jicheng.A New Preconditioner for Solving Weighted Toeplitz Least Squares Problems[J].Mathematica Applicata,2020,33(1):172-185. |
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| Authors: | CHENG Guo LI Jicheng |
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| Institution: | (School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China;School of Mathematics and Computer Application,Shangluo University,Shangluo 726000,China) |
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| Abstract: | 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. |
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| Keywords: | Least squares problem Weighted Toeplitz matrix Preconditioner Hermitian and skew-Hermitian splitting |
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