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- Tikhonov_regularization abstract "Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems. In statistics, the method is known as ridge regression, and, with multiple independent discoveries, it is also variously known as the Tikhonov–Miller method, the Phillips–Twomey method, the constrained linear inversion method, and the method of linear regularization. It is related to the Levenberg–Marquardt algorithm for non-linear least-squares problems.When the following problem is not well posed (either because of non-existence or non-uniqueness of ) then the standard approach is known as ordinary least squares and seeks to minimize the residual where is the Euclidean norm. This may be due to the system being overdetermined or underdetermined (may be ill-conditioned or singular). In the latter case this is no better than the original problem. In order to give preference to a particular solution with desirable properties, the regularization term is included in this minimization: for some suitably chosen Tikhonov matrix, . In many cases, this matrix is chosen as the identity matrix , giving preference to solutions with smaller norms. In other cases, lowpass operators (e.g., a difference operator or a weighted Fourier operator) may be used to enforce smoothness if the underlying vector is believed to be mostly continuous.This regularization improves the conditioning of the problem, thus enabling a direct numerical solution. An explicit solution, denoted by , is given by: The effect of regularization may be varied via the scale of matrix . For this reduces to the unregularized least squares solution provided that (ATA)−1 exists.".
- Tikhonov_regularization wikiPageExternalLink pg=1006.
- Tikhonov_regularization wikiPageExternalLink index.html.
- Tikhonov_regularization wikiPageExternalLink golub.heath.wahba.pdf).
- Tikhonov_regularization wikiPageID "954323".
- Tikhonov_regularization wikiPageRevisionID "606337549".
- Tikhonov_regularization hasPhotoCollection Tikhonov_regularization.
- Tikhonov_regularization subject Category:Estimation_theory.
- Tikhonov_regularization subject Category:Inverse_problems.
- Tikhonov_regularization subject Category:Linear_algebra.
- Tikhonov_regularization comment "Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems. In statistics, the method is known as ridge regression, and, with multiple independent discoveries, it is also variously known as the Tikhonov–Miller method, the Phillips–Twomey method, the constrained linear inversion method, and the method of linear regularization.".
- Tikhonov_regularization label "Regolarizzazione di Tichonov".
- Tikhonov_regularization label "Regularización de Tíjonov".
- Tikhonov_regularization label "Régularisation Tychonoff".
- Tikhonov_regularization label "Tikhonov regularization".
- Tikhonov_regularization sameAs Regularización_de_Tíjonov.
- Tikhonov_regularization sameAs Régularisation_Tychonoff.
- Tikhonov_regularization sameAs Regolarizzazione_di_Tichonov.
- Tikhonov_regularization sameAs m.03t125.
- Tikhonov_regularization sameAs Q2778212.
- Tikhonov_regularization sameAs Q2778212.
- Tikhonov_regularization wasDerivedFrom Tikhonov_regularization?oldid=606337549.
- Tikhonov_regularization isPrimaryTopicOf Tikhonov_regularization.