Investigation of Preconditioning Techniques for the Iteratively Regularized Gauss-Newton Method for Exponentially Ill-Posed Problems

Authors:
Stefan Langer
Affiliations:
stefan.langer@dlr.de
Venue:
SIAM Journal on Scientific Computing
Year:
2010

Citing 8
Cited 1

The problem of the convergence of the iteratively regularized Gauss-Newton method

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Iterative solution methods

Iterative solution methods
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Which Eigenvalues Are Found by the Lanczos Method?

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Fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem

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Abstract

We examine preconditioning techniques for exponentially ill-posed problems which significantly reduce the total complexity of regularized Newton methods. The construction of the preconditioners exploits the close connection of the CG method, which is applied to solve the linear systems, and Lanczos' method, which is used to determine spectral data to construct and update spectral preconditioners. In examples from acoustic and electromagnetic scattering problems we show the superiority of our preconditioned Newton methods when compared with other kinds of Newton methods.