基于奇异值分解建立的一种新的正则化方法

数学物理学报 ›› 2005, Vol. 25 ›› Issue (3): 331-336.

基于奇异值分解建立的一种新的正则化方法

黄小为, 吴传生, 朱华平

武汉理工大学理学院\ 武汉武汉大学软件工程国家重点实验室武汉

出版日期:2005-07-24 发布日期:2005-07-24

A New Regularization Method Based on the Singular Value Decomposition for Compact Operators

HUANG Xiao-Wei, TUN Chuan-Sheng, SHU Hua-Beng-

Online:2005-07-24 Published:2005-07-24

摘要/Abstract

摘要：

根据紧算子的奇异系统理论，引入一种正则化滤子函数，从而建立一种新的正则化方法来求解右端近似给定的第一类算子方程，并给出了正则解的误差分析。通过正则参数的先验选取，证明了正则解的误差具有渐进最优阶。 

关键词: 不适定问题,正则化滤子函数,正则化方法;渐进最优阶.

Abstract:

According to the theory of singular system of compact operators, a new regulariz ation filters is set forth, and then a new regularization method for solving illposed problems of the first kind equations is constructed. The error analysis o f the regularized solution is given. By a priori choice of the regularization pa rameter respectively, the optimum asymptotic convergence order of the regularize d solution is obtained.

Key words: problems;Regularization filters;Regulariz ation method;Convergence and asymptotic order of the regularized solution

中图分类号:

65J20

黄小为, 吴传生, 朱华平. 基于奇异值分解建立的一种新的正则化方法[J]. 数学物理学报, 2005, 25(3): 331-336.

HUANG Xiao-Wei, TUN Chuan-Sheng, SHU Hua-Beng-. A New Regularization Method Based on the Singular Value Decomposition for Compact Operators[J]. Acta mathematica scientia,Series A, 2005, 25(3): 331-336.