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

An approximately globally convergent numerical method proposed by Beilina and Klibanov for a coefficient inverse problem related to the hyperbolic equation c(x)u(tt) = u(xx) is studied. While the global convergence of this method has been proved for the 3D case, in 1D case, it was proved only partially. The last case is of an interest, since it was demonstrated that the 1D version of this method works well for a set of experimental data. In this paper, a complete proof of convergence of this method in 1D is presented.