The authors are concerned with a regularization method for the problem of recovering the index of refraction n in the inhomogeneous reduced wave equation ( Delta +k2n2(x))u(x)=F(x) x in Omega where Omega is a domain in R3 and k>0 is given. Assuming a known solution u of the above equation, they consider a fixed finite dimensional variational inequality that is supposed to approximate the original problem. Then, by an asymptotic regularization method, they construct by iteration a sequence of stable, finite dimensional variational inequalities, solutions of which are shown to converge to a solution of the above finite dimensional variational inequality.
