Abstract
The method of Tikhonov regularization for stabilizing inverse problem solutions is introduced and illustrated with examples. Zeroth-order Tikhonov regularization is explored, including its resolution, bias, and uncertainty properties. The concepts of filter factors (which control the contribution of singular values and their corresponding singular vectors to the solution) and the discrepancy and L-curve criteria (strategies for selecting the regularization parameter) are presented. Higher-order Tikhonov regularization techniques and their computation by the generalized SVD (GSVD) and truncated GSVD are discussed. Generalized cross-validation is introduced as an alternative method for selecting the regularization parameter. Theorems for bounding the error in the regularized solution are discussed. The BVLS method for applying strict upper and lower bounds to least-squares solutions is introduced.
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