Solution of Ill-Posed Problems by Means of Truncated SVD
Solution of Ill-Posed Problems by Means of Truncated SVD
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DOI：
10.1007/978-3-0348-6303-2_15
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发表时间：
1988-06
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影响因子：
--
通讯作者：
P. Hansen
中科院分区：
文献类型：
--
作者：
P. Hansen
本文研究了具有良定和病态秩矩阵的不适定最小二乘问题的截断奇异值分解（TSVD）解。如果满足离散Picard条件，则在这两种情况下都可以选择截断参数，使得TSVD解是令人满意的。适当的截断参数，在解决方案中给出最佳的信噪比，是广义交叉验证函数的最小值。
We considerTruncated SVD(TSVD) solutions to ill-posed least squares problems involving matrices with well-determined as well as ill-determined numerical rank. If adiscrete Picard conditionis satisfied, then inboth casesthe truncation parameter can be chosen such that the TSVD solution is satisfactory. The appropriate truncation parameter, giving the optimal signal-to-noise ratio in the solution, is the minimizer of the generalized cross-validation function.