Tikhonov正则化
数学
巴克斯-吉尔伯特法
正规化(语言学)
系数矩阵
应用数学
支持向量机的正则化研究进展
反问题
最小二乘函数近似
线性最小二乘法
基质(化学分析)
数学分析
数学优化
线性模型
特征向量
计算机科学
统计
物理
人工智能
估计员
材料科学
量子力学
复合材料
作者
Gene H. Golub,Per Christian Hansen,Dianne P. O’Leary
标识
DOI:10.1137/s0895479897326432
摘要
Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to computestable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov's regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation suited for problems in which both the coefficient matrix and the right-hand side are known only approximately. We analyze the regularizing properties of this method and demonstrate by a numerical example that, in certain cases with large perturbations, the new method is superior to standard regularization methods.
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