Extended Newton-type iteration for nonlinear ill-posed equations in Banach space

In this paper, we study nonlinear ill-posed equations involving m -accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. Using general Hölder type...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 60; no. 1-2; pp. 435 - 453
Main Authors: Sreedeep, C. D., George, Santhosh, Argyros, Ioannis K.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
Springer Nature B.V
Subjects:
Applied mathematics
Banach spaces
Computational Mathematics and Numerical Analysis
Ill posed problems
Mathematical analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear equations
Original Research
Parameters
Regularization
Theory of Computation
Accretive mappings
49J30
Extended Newton iterative scheme
Adaptive parameter choice strategy
Lavrentiev regularization
47J05
47J06
65J20
Nonlinear ill-posed problem
Banach space
47H06
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:In this paper, we study nonlinear ill-posed equations involving m -accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076,  2005 ) for choosing the regularization parameter.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-018-01221-2