A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations

2015 ◽  
Vol 254 ◽  
pp. 148-156 ◽  
Author(s):  
P. Jidesh ◽  
Vorkady S. Shubha ◽  
Santhosh George
Keyword(s):  
Iterative Method ◽  
Regularization Method ◽  
Quadratic Convergence ◽  
Lavrentiev Regularization ◽  
Ill Posed ◽  
Lavrentiev Regularization Method

An iterative Lavrentiev regularization method

2006 ◽  
Vol 46 (3) ◽  
pp. 589-606 ◽  
Author(s):  
S. Morigi ◽  
L. Reichel ◽  
F. Sgallari
Keyword(s):  
Regularization Method ◽  
Lavrentiev Regularization ◽  
Lavrentiev Regularization Method

A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations

2012 ◽  
Vol 12 (1) ◽  
pp. 32-45 ◽  
Author(s):  
Santhosh George ◽  
Atef Ibrahim Elmahdy
Keyword(s):  
Iterative Method ◽  
Operator Equation ◽  
Quadratic Convergence ◽  
Regularization Parameter ◽  
Optimal Order ◽  
Majorizing Sequence ◽  
Operator Equations ◽  
Order Error ◽  
Ill Posed ◽  
The Given

AbstractIn this paper, we consider an iterative method for the approximate solution of the nonlinear ill-posed operator equation Tx = y. The iteration procedure converges quadratically to the unique solution of the equation for the regularized approximation. It is known that (Tautanhahn (2002)) this solution converges to the solution of the given ill-posed operator equation. The convergence analysis and the stopping rule are based on a suitably constructed majorizing sequence. We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining an optimal order error estimate.

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.

scholarly journals Heating source localization in a reduced time

2016 ◽  
Vol 26 (3) ◽  
pp. 623-640 ◽  
Author(s):  
Sara Beddiaf ◽  
Laurent Autrique ◽  
Laetitia Perez ◽  
Jean-Claude Jolly
Keyword(s):  
Heat Conduction ◽  
Source Localization ◽  
Conjugate Gradient ◽  
Regularization Method ◽  
Three Dimensional ◽  
Gradient Algorithm ◽  
Iterative Regularization ◽  
Heating Source ◽  
Ill Posed ◽  
Reduced Time

Abstract Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

Sign in / Sign up

Export Citation Format

Share Document