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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Iterative processes of gradient type with applications to gravimetry and magnetometry inverse problems

1Department of Ill-Posed Problems and Applications, Institute of Mathematics and Mechanics UB RAS, S. Kovalevskaya Street 16, Ekaterinburg 620990, Russia.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 8, Pages 855–876, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.007, April 2011

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The iterative processes of gradient type for nonlinear equations with differentiable operator satisfying a local condition in the neighborhood of solution are investigated. The theorems on weak and strong convergence of iterations constructed by these methods and their modified analogs are established.

The inverse gravimetry problem is considered as the application of the developed methods: retrieval of the interface between the media with different constant densities. For stable solution of the nonlinear inverse magnetometry problem the additional regularization by the Tikhonov method is used and for approximation of the regularized solution one variant of the conjugate gradient method is applied. The numerical results for model and real gravitational and magnetic data are considered.

Keywords.: Methods of gradient type; local condition; pseudo-contractive mapping; Tikhonov regularization; inverse gravimetry and magnetometry problems

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