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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 11, Issue 1 (Mar 2003)


Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation

S. I. Kabanikhin
  • Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mail:
/ O. Scherzer
  • Department of Computer Science, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria. E-mail: .
/ M. A. Shishlenin
  • Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia.

In this paper we study the problem of estimating a two-dimensional parameter in the wave equation from overdetermined observational boundary data. The inverse problem is reformulated as an integral equation and two numerical algorithms, the projection method and the Landweber iteration method are investigated. By the projection method the inverse problem is reduced to a finite dimensional system of integral equations. We prove convergence of the projection method. Moreover, we show that the Landweber iteration method is a stable and convergent numerical method for solving this parameter estimation problem.

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Published in Print: 2003-03-01

Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939403322004955.

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Sergey I. Kabanikhin and Maxim A. Shishlenin
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