This paper seeks to identify the coefficient v in the steady-state diffusion equa-tion -div(v gradu) = f for two dimensional anisotropic medium in a boundeddomain Ω from two known solutions u1, u2 of the corresponding Dirichlet prob-lems, where f is known, v takes diagonal matrix values, which are given at theboundary of Ω, and may have mild discontinuities. This problem is solved byminimization of an associated functional. We propose an alternating Neubergergradient algorithm, and show the results of numerical experiments.