Convergence theorem for a numerical method of a 1D coefficient inverse problem

Abstract

An approximately globally convergent numerical method proposed by Beilina and Klibanov for a coefficient inverse problem related to the hyperbolic equation is studied. While the global convergence of this method has been proved for the case, in case, it was proved only partially. The last case is of an interest, since it was demonstrated that the version of this method works well for a set of experimental data. In this paper, a complete proof of convergence of this method in is presented.

Keywords:

• coefficient inverse problem
• hyperbolic equation
• numerical method
• convergence theorem

AMS Subject Classifications:

• 35L20
• 65M32

Acknowledgements

The authors would like to thank Professor Alemdar Hasanoglu for the formulation of the problem and for his valuable comments and suggestions leading to a better presentation of this article.