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

Abstract

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.