A numerical method for solving nonlinear ill-posed problems

A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization parameter is introduced. A convergence theorem is proved. The proposed method is illustrated by a numerical ex...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 20; no. 3-4; pp. 317 - 332
Main Authors: Ramm, Alexander G., Smirnova, Alexandra B.
Format: Journal Article
Language:English
Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1999
Taylor & Francis
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Fréchet derivative
ill-posed problem
Mathematical analysis
Mathematics
Partial differential equations
regularization
Sciences and techniques of general use
Two-step iterative method
Non linear equation
Simpson formula
Operator equation
Frechet derivative
A2 method
Hilbert space
Ill posed problem
Frechet differentiability
Regularization
Solvability
Partial differential equation
Convergence
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization parameter is introduced. A convergence theorem is proved. The proposed method is illustrated by a numerical example in which a nonlinear inverse problem of gravimetry is considered. Based on the results of the numerical experiments practical recommendations for the choice of the regularization parameter are given. Some other iterative schemes are considered.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630569908816894