Tikhonov regularization and total least squares
Tikhonov regularization and total least squares
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DOI：
10.1137/s0895479897326432
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发表时间：
1999-10-27
影响因子：
1.5
通讯作者：
O'Leary, DP
中科院分区：
文献类型：
--
作者：
Golub, GH;Hansen, PC;O'Leary, DP
反问题的离散化导致具有高度病态系数矩阵的线性方程组，并且为了计算这些系统的稳定解，有必要应用正则化方法。我们展示了如何吉洪诺夫的正则化方法，在其原来的配方涉及一个最小二乘问题，可以重铸在一个总的最小二乘配方适合的问题，其中系数矩阵和右手边只知道近似。我们分析了这种方法的正则化性质，并通过数值例子证明，在某些情况下，大扰动，新的方法是上级优于标准的正则化方法。
Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable 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.