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An iterative regularization method for ill-posed Hammerstein type operator equation
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S. George
Published/Copyright:
January 26, 2010
Abstract
A combination of Newton's method and a regularization method has been considered for obtaining a stable approximate solution for ill-posed Hammerstein type operator equation. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (SIAM. J. Numer. Anal. 43: 2060–2076, 2005) an order optimal error estimate has been obtained. Moreover the method that we consider gives quadratic convergence compared to the linear convergence obtained by George and Nair (J. Complexity 24: 228–240, 2008).
Key words.: Nonlinear ill-posed equations; Hammerstein type equations; iterative regularization; adaptive choice
Received: 2009-05-10
Published Online: 2010-01-26
Published in Print: 2009-December
© de Gruyter 2009
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Articles in the same Issue
- An iterative regularization method for ill-posed Hammerstein type operator equation
- Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization
- Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration
- Regularization methods for a Cauchy problem for a parabolic equation in multiple dimensions
- A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem
Keywords for this article
Nonlinear ill-posed equations;
Hammerstein type equations;
iterative regularization;
adaptive choice
Articles in the same Issue
- An iterative regularization method for ill-posed Hammerstein type operator equation
- Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization
- Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration
- Regularization methods for a Cauchy problem for a parabolic equation in multiple dimensions
- A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem
