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Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation
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S. I. Kabanikhin
Published/Copyright:
2003
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.
Published Online: --
Published in Print: 2003-03-01
Copyright 2003, Walter de Gruyter
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- Inverse problems and classes of solutions of evolution equations
- Planar crack identification for the transient heat equation
- Parameter identification for Laplace equation and approximation in Hardy classes
- Determination of the memory kernel from boundary measurements on a finite time interval
- Parabolic integro-differential identification problems related to memory kernels with special symmetries
- Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation
Articles in the same Issue
- Inverse problems and classes of solutions of evolution equations
- Planar crack identification for the transient heat equation
- Parameter identification for Laplace equation and approximation in Hardy classes
- Determination of the memory kernel from boundary measurements on a finite time interval
- Parabolic integro-differential identification problems related to memory kernels with special symmetries
- Iteration methods for solving a two dimensional inverse problem for a hyperbolic equation
