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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2013, Volume 6, Issue 3, Pages 26–37 (Mi vyuru3)  

Mathematical Modelling

Iterative Newton Type Algorithms and Its Applications to Inverse Gravimetry Problem

V. V. Vasinab, E. N. Akimovaab, A. F. Miniakhmetovaab

a Institute of Mathematics and Mechanics of UrB RAS
b Ural Federal University, Ekaterinburg, Russian Federation

Abstract: The paper gives a brief overview of approaches to the construction of iterative processes of the Newton and gradient type for stable approximation of solutions to nonlinear irregular operator equations in Hilbert spaces. For two-stage algorithms based on Lavrentiev regularization scheme and a modified Newton's method the convergence theorem are formulated and the results of numerical solution to three-dimensional inverse gravimerty problem for two-layer model are discussed.

Keywords: irregular operator equation, modified Newton method, inverse gravimetry problem.

Full text: PDF file (503 kB)
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UDC: 517.988.68
MSC: 45Q, 65N20
Received: 15.05.2013

Citation: V. V. Vasin, E. N. Akimova, A. F. Miniakhmetova, “Iterative Newton Type Algorithms and Its Applications to Inverse Gravimetry Problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013), 26–37

Citation in format AMSBIB
\Bibitem{VasAkiMin13}
\by V.~V.~Vasin, E.~N.~Akimova, A.~F.~Miniakhmetova
\paper Iterative Newton Type Algorithms and Its Applications to Inverse Gravimetry Problem
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2013
\vol 6
\issue 3
\pages 26--37
\mathnet{http://mi.mathnet.ru/vyuru3}


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