地球物理反问题中两种正则化方法的比较  

Comparison Between Tikhonov Regularization and Truncated SVD in Geophysics

作　　者：顾勇为[1] 归庆明[1] 边少锋[2] 郭建峰[1] 

机构地区：[1]信息工程大学理学院数理系 [2]海军工程大学四系,武汉市解放大道339号430033

出　　处：《武汉大学学报（信息科学版）》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)

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.

关 键 词：正则化方法 良定秩 劣定秩 

分 类 号：P223[天文地球—大地测量学与测量工程]