Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales
Keyword(s):
Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equationF(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 onx0-x^(x0is the initial guess andx^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.
2014 ◽
Vol 2014
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pp. 1-8
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2012 ◽
Vol 12
(1)
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pp. 32-45
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2018 ◽
Vol 18
(2)
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pp. 313-321
Keyword(s):
2017 ◽
Vol 8
(4)
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pp. 342
2020 ◽
Vol 20
(2)
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pp. 321-341