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Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales
Joint Authors
Shobha, Monnanda Erappa
George, Santhosh
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-01
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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 method considered by Vasin and George (2013), in the setting of Hilbert scales.
The error estimates obtained under a general source condition on x0-x^ (x0 is the initial guess and x^ is the actual solution), using the adaptive scheme proposed by Pereverzev and Schock (2005), are of optimal order.
The algorithm is applied to numerical solution of an integral equation in Numerical Example section.
American Psychological Association (APA)
Shobha, Monnanda Erappa& George, Santhosh. 2014. Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales. Journal of Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1041112
Modern Language Association (MLA)
Shobha, Monnanda Erappa& George, Santhosh. Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales. Journal of Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1041112
American Medical Association (AMA)
Shobha, Monnanda Erappa& George, Santhosh. Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales. Journal of Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1041112
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1041112