Results 21 to 30 of about 2,383 (165)

Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales

Journal of Mathematics, 2014
Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equation F(x)=y. In order to improve the error estimate available by Vasin and George (2013), in the present paper we extend the iterative ...
Monnanda Erappa Shobha, Santhosh George
doaj   +1 more source

A numerical method for solving nonlinear ill-posed problems [PDF]

Numerical Functional Analysis and Optimization, 1999
A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Frechet derivative operator, some regularization parameter is introduced. A convergence theorem is proved.
Alexander G. Ramm, Alexandra B. Smirnova
openaire   +1 more source

Simultaneous reconstruction of time-dependent coefficients in the parabolic equation from over-specification conditions

Results in Applied Mathematics, 2021
The inverse problem of reconstructing the time-dependent coefficients, along with the temperature in a one-dimensional parabolic equation with initial and Neumann boundary conditions supplemented by non-local integral and boundary specification ...
M.J. Huntul
doaj   +1 more source

Coordinated approximation method for nonlinear ill-posed problems [PDF]

Ukrainian Mathematical Journal, 1994
Summary: A generalization of the method of coordinated approximation suggested by \textit{Yu. Gaponenko} [Ill-posed problems on weak compacta (1989; Zbl 0696.65053)] for the space \(L_2(0, 1)\) is developed for abstract Hilbert spaces. In particular, it is shown that, for \(L_2(0, 1)\), some assumptions concerning an exact solution can be weakened.
openaire   +2 more sources

A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces

Journal of Numerical Analysis and Approximation Theory
One popular regularization technique for handling both linear and nonlinear ill-posed problems is homotopy perturbation. In order to solve nonlinear ill-posed problems, we investigate an iteratively-regularized simplified version of the Homotopy ...
Sharad Kumar Dixit
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A Pinning Actor-Critic Structure-Based Algorithm for Sizing Complex-Shaped Depth Profiles in MFL Inspection with High Degree of Freedom

Complexity, 2021
One of the most efficient nondestructive methods for pipeline in-line inspection is magnetic flux leakage (MFL) inspection. Estimating the size of the defect from MFL signal is one of the key problems of MFL inspection.
Zhenning Wu, Yiming Deng, Lixing Wang
doaj   +1 more source

Majorization–Minimization Total Variation Solution Methods for Electrical Impedance Tomography

Mathematics, 2022
Inverse problems arise in many areas of science and engineering, such as geophysics, biology, and medical imaging. One of the main imaging modalities that have seen a huge increase in recent years is the noninvasive, nonionizing, and radiation-free ...
Eman Alruwaili, Jing Li
doaj   +1 more source

Continuous regularization of nonlinear ill-posed problems

, 1999
A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the original nonlinear stationary problem. Examples of applications of the general method are given. Convergence theorems
Airapetyan, R., Ramm, A. G., Smirnova, A.   +2 more
openaire   +2 more sources

Parameter Choice Strategy That Computes Regularization Parameter before Computing the Regularized Solution

Modelling
The modeling of many problems of practical interest leads to nonlinear ill-posed equations (for example, the parameter identification problem (see the Numerical section)).
Santhosh George, Jidesh Padikkal, Ajil Kunnarath, Ioannis K. Argyros, Samundra Regmi   +4 more
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Choice of Regularization Methods in Experiment Processing: Solving Inverse Problems of Thermal Conductivity

Mathematics, 2022
This work is aimed at numerical studies of inverse problems of experiment processing (identification of unknown parameters of mathematical models from experimental data) based on the balanced identification technology.
Alexander Sokolov, Irina Nikulina
doaj   +1 more source