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Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration
Published/Copyright:
January 26, 2010
Abstract
In this paper we investigate the numerical complexity to solve nonlinear ill-posed problems when the operator equations F(x) = yδ are solved by the iteratively regularized Gauss–Newton method (IRGNM) with inner CG-iteration. Additionally we consider a preconditioned version of the IRGNM and compare the complexity of the standard IRGNM and its preconditioned version. In the case of exponentially ill-posed problems we show the superiority of the preconditioned IRGNM, that is we prove that the preconditioning techniques presented in this paper yield a significant reduction of the total complexity.
Received: 2009-04-07
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 inverse problems;
regularized Newton methods;
CG-method;
complexity analysis
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
