摘要
通过对最小二乘法的改造引入了两种正则化方法及其解的表达式,从理论上阐述了 Tikhonov与 TS- VD两种正则化方法效果的差异,特别就病态方程组在三种情况———系数阵良定秩、系数阵劣定秩右端项劣衰减、系数阵劣定秩右端项良衰减下正则化方法的应用效果作了比较,并给出了数值例子。
Ill-posed problem often appears in the inverse problem in geophysics. Many regularization methods are used to produce reasonable solutions. Among them, Tikhonov regularization and truncated SVD (Singular Value Decomposition) are two important methods used widely, but how to compare them is a challenging and meaningful area under discussion. The paper discusses the comparison between them. First, with the SVD of coefficients matrix, the ordinary least squares (LS) solution to linear equation is expressed by decomposition of pseudo-inverse of the matrix. Then, through the analysis of the parameters, the similarity and difference between the two methods are declared theoretically. Last, some numerical examples are given to confirm the theory.
出处
《武汉大学学报(信息科学版)》
EI
CSCD
北大核心
2005年第3期238-241,共4页
Geomatics and Information Science of Wuhan University
基金
国家杰出青年科学基金资助项目(40125013)
国家自然科学基金资助项目(40074006)
关键词
正则化方法
良定秩
劣定秩
regularization
well-defined rank
bad determined rank