顾勇为, 归庆明, 边少锋, 郭建峰. 地球物理反问题中两种正则化方法的比较[J]. 武汉大学学报 ( 信息科学版), 2005, 30(3): 238-241.
引用本文: 顾勇为, 归庆明, 边少锋, 郭建峰. 地球物理反问题中两种正则化方法的比较[J]. 武汉大学学报 ( 信息科学版), 2005, 30(3): 238-241.
GU Yongwei, GUI Qingming, BIAN Shaofeng, GUO Jianfeng. Comparison Between Tikhonov Regularization and Truncated SVD in Geophysics[J]. Geomatics and Information Science of Wuhan University, 2005, 30(3): 238-241.
Citation: GU Yongwei, GUI Qingming, BIAN Shaofeng, GUO Jianfeng. Comparison Between Tikhonov Regularization and Truncated SVD in Geophysics[J]. Geomatics and Information Science of Wuhan University, 2005, 30(3): 238-241.

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

  • 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。

     

    Abstract: 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) solu

     

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