scholarly journals The Tikhonov Regularization Method for Set-Valued Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yiran He
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Existence Result ◽  
Tikhonov Regularization Method ◽  
Regularization Theory ◽  
Coercivity Condition ◽  
General Existence

This paper aims to establish the Tikhonov regularization theory for set-valued variational inequalities. For this purpose, we firstly prove a very general existence result for set-valued variational inequalities, provided that the mapping involved has the so-called variational inequality property and satisfies a rather weak coercivity condition. The result on the Tikhonov regularization improves some known results proved for single-valued mapping.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document