GCV for Tikhonov regularization via global Golub–Kahan decomposition
نویسندگان
چکیده
منابع مشابه
GCV for Tikhonov regularization via global Golub-Kahan decomposition
Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...
متن کاملLearning a regression function via Tikhonov regularization
We consider the problem of estimating a regression function on the basis of empirical data. We use a Reproducing Kernel Hilbert Space (RKHS) as our hypothesis space, and we follow the methodology of Tikhonov regularization. We show that this leads to a learning scheme that is different from the one usually considered in Learning Theory. Subject to some regularity assumptions on the regression f...
متن کاملTikhonov regularization via flexible Arnoldi reduction
Flexible GMRES, introduced by Saad, is a generalization of the standard GMRES method for the solution of large linear systems of equations. It is based on the flexible Arnoldi process for reducing a large square matrix to a small matrix. We describe how the flexible Arnoldi process can be applied to implement one-parameter and multi-parameter Tikhonov regularization of linear discrete ill-posed...
متن کاملA Regularization Parameter for Nonsmooth Tikhonov Regularization
In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...
متن کاملTikhonov Regularization
An important issue in quantitative nance is model calibration. The calibration problem is the inverse of the pricing problem. Instead of computing prices in a model with given values for its parameters, one wishes to compute the values of the model parameters that are consistent with observed prices. Now, it is well-known by physicists that such inverse problems are typically ill-posed. So, if ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2016
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.2034