caa a22 4500 378870351 CHVBK 20180305123407.0 cr unu---uuuuu 161128e20030301xx s 000 0 eng 10.1515/156939403322004955 doi (NATIONALLICENCE)gruyter-10.1515/156939403322004955 Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation [Elektronische Daten] [S. I. Kabanikhin, O. Scherzer, M. A. Shishlenin] 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. Copyright 2003, Walter de Gruyter Kabanikhin S. I. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mail: kabanikh@math.nsc.ru aut Scherzer O. Department of Computer Science, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria. E-mail: otmar.scherzer@uibk.ac.at. aut Shishlenin M. A. Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia. aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/1(2003-03-01), 87-109 0928-0219 11:1<87 2003 11 jiip https://doi.org/10.1515/156939403322004955 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403322004955 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kabanikhin S. I. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mail: kabanikh@math.nsc.ru aut NATIONALLICENCE 700 1- Scherzer O. Department of Computer Science, University of Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria. E-mail: otmar.scherzer@uibk.ac.at aut NATIONALLICENCE 700 1- Shishlenin M. A. Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/1(2003-03-01), 87-109 0928-0219 11:1<87 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter