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786
TIKHONOV REGULARIZATION
, 2008
"... 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 ..."
Abstract
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switches from one `basin of attraction ' to the other, thus the numerically determined solution isunstable. To achieve robustness of model (re)calibration, we need to introduce some regularization. The most widely known and applicable regularization method is Tikhonov ( Phillips) regularization method
Arnoldi-Tikhonov regularization methods
, 2008
"... Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. C ..."
Abstract
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Cited by 11 (8 self)
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Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix
Nonstationary Iterated Tikhonov Regularization
"... A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. It is also shown that an order-optimal accuracy is attained when a certain a p ..."
Abstract
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Cited by 22 (1 self)
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A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. It is also shown that an order-optimal accuracy is attained when a certain a
Training with Noise is Equivalent to Tikhonov Regularization
- Neural Computation
, 1994
"... It is well known that the addition of noise to the input data of a neural network during training can, in some circumstances, lead to significant improvements in generalization performance. Previous work has shown that such training with noise is equivalent to a form of regularization in which an ex ..."
Abstract
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Cited by 158 (0 self)
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of network training, the regularization term can be reduced to a positive definite form which involves only first derivatives of the network mapping. For a sum-of-squares error function, the regularization term belongs to the class of generalized Tikhonov regularizers. Direct minimization of the regularized
Tikhonov regularization with a solution constraint
- SIAM J. Sci. Comput
"... Abstract. Many numerical methods for the solution of linear ill-posed problems apply Tikhonov regularization. This paper presents a modification of a numerical method proposed by Golub and von Matt for quadratically constrained least-squares problems and applies it to Tikhonov regularization of larg ..."
Abstract
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Cited by 13 (6 self)
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Abstract. Many numerical methods for the solution of linear ill-posed problems apply Tikhonov regularization. This paper presents a modification of a numerical method proposed by Golub and von Matt for quadratically constrained least-squares problems and applies it to Tikhonov regularization
A new Tikhonov regularization method
- Numer. Algorithms
"... Abstract. The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for problems of small to moderate size, which allow evaluat ..."
Abstract
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Cited by 3 (2 self)
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evaluation of the singular value decomposition of the matrix defining the problem, are the truncated singular value decomposition and Tikhonov regularization. The present paper proposes a novel choice of regularization matrix for Tikhonov regularization that bridges the gap between Tikhonov regularization
Edge detection method by Tikhonov regularization
- Proceedings of 14 International Conference GraphiCon`2004
, 2004
"... Image restoration is one of the classical inverse problems in image processing and computer vision, which consists in recovering information about the original image from incomplete or degraded data. This paper presents analytical solution for onedimensional case of the Tikhonov regularization metho ..."
Abstract
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Cited by 1 (1 self)
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Image restoration is one of the classical inverse problems in image processing and computer vision, which consists in recovering information about the original image from incomplete or degraded data. This paper presents analytical solution for onedimensional case of the Tikhonov regularization
Tikhonov regularization with nonnegativity constraint, Electron
- Trans. Numer. Anal
"... Abstract. Many numerical methods for the solution of ill-posed problems are based on Tikhonov regularization. Recently, Rojas and Steihaug [15] described a barrier method for computing nonnegative Tikhonov-regularized approximate solutions of linear discrete ill-posed problems. Their method is based ..."
Abstract
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Cited by 7 (3 self)
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Abstract. Many numerical methods for the solution of ill-posed problems are based on Tikhonov regularization. Recently, Rojas and Steihaug [15] described a barrier method for computing nonnegative Tikhonov-regularized approximate solutions of linear discrete ill-posed problems. Their method
Results 1 - 10
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786
