A new choice rule for regularization parameters in Tikhonov regularization

2011 ◽  
Vol 90 (10) ◽  
pp. 1521-1544 ◽  
Author(s):  
Kazufumi Ito ◽  
Bangti Jin ◽  
Jun Zou
Keyword(s):  
Tikhonov Regularization ◽  
Choice Rule ◽  
Regularization Parameters

scholarly journals On the Local Regularization of Inverse Problems of Volterra Type

1995 ◽  
Author(s):  
Patricia K. Lamm
Keyword(s):  
Tikhonov Regularization ◽  
Volterra Operator ◽  
Dimensional Regularization ◽  
Convergence Theory ◽  
True Solution ◽  
Infinite Dimensional ◽  
Local Regularization ◽  
Regularization Parameters ◽  
Regularization Problem ◽  
Local Procedure

Abstract We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include the standard Tikhonov parameter, as well as a parameter that represents the length of the local regularization interval. We present a convergence theory for the infinite-dimensional regularization problem and show that the regularized solutions converge to the true solution as the regularization parameters go to zero (in a prescribed way). In addition, we show how numerical implementation of the ideas of local regularization can lead to the notion of “sequential Tikhonov regularization” for Volterra problems; this approach has been shown in (Lamm and Eldén, 1995) to be just as effective as Tikhonov regularization, but to be much more efficient computationally.

Scattered data fitting by minimal surface

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Yong-Xia Hao ◽  
Dianchen Lu
Keyword(s):  
Tikhonov Regularization ◽  
Numerical Experiments ◽  
Data Fitting ◽  
Scattered Data ◽  
B Spline ◽  
Scattered Data Fitting ◽  
Area Minimization ◽  
Regularization Parameters ◽  
The Given ◽  
Minimal Area

AbstractThe goal of this paper is to develop a computational model for obtaining the fitting surface to the given scattered data with minimal area. The basic idea of the model is to utilize the B-spline and area minimization. The model is turned into a Tikhonov regularization model finally. By choosing the regularization parameters with the L-curve criterion and the GCV method, respectively, numerical experiments indicate that the model can provide an acceptable compromise between the minimization of the data mismatch term and the area of the surface.

scholarly journals DISCREPANCY SETS FOR COMBINED LEAST SQUARES PROJECTION AND TIKHONOV REGULARIZATION

2017 ◽  
Vol 22 (2) ◽  
pp. 202-212
Author(s):  
Teresa Reginska
Keyword(s):  
Least Squares ◽  
Tikhonov Regularization ◽  
Discrepancy Principle ◽  
Order Of Accuracy ◽  
Finite Dimensional ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Data Error ◽  
Two Parameter ◽  
Regularized Solution

To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepancy set for any data error bound. The aim of the paper is to describe this set and to indicate its subset such that for regularization parameters from this subset the related regularized solution has the same order of accuracy as the Tikhonov regularization with the standard discrepancy principle but without any discretization.

Dual Regularized Total Least Squares And Multi-Parameter Regularization

2008 ◽  
Vol 8 (3) ◽  
pp. 253-262 ◽  
Author(s):  
S. LU ◽  
S.V. PEREVERZEV ◽  
U. TAUTENHAHN
Keyword(s):  
Least Squares ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Differential Operators ◽  
Total Least Squares ◽  
Right Hand ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Regularized Total Least Squares ◽  
Parameter Regularization

AbstractIn this paper we continue our study of solving ill-posed problems with a noisy right-hand side and a noisy operator. Regularized approximations are obtained by Tikhonov regularization with differential operators and by dual regularized total least squares (dual RTLS) which can be characterized as a special multi-parameter regularization method where one of the two regularization parameters is negative. We report on order optimality results for both regularized approximations, discuss compu-tational aspects, provide special algorithms and show by experiments that dual RTLS is competitive to Tikhonov regularization with differential operators.

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