A CONVERGENT RECONSTRUCTION METHOD FOR AN ELLIPTIC OPERATOR IN POTENTIAL FORM

We investigate the problem of recovering a potential q(x) in the equat ion -Delta u + q(x)u = 0 from overspecified boundary data on the unit square in R(2). The potential is characterized as a fixed point of a n onlinear operator, which is shown to be a contraction on a ball in C-a lpha. Uniqueness of q(x) follows, as does convergence of the resulting recovery scheme. Numerical examples, demonstrating the performance of the algorithm, are presented. (C) 1995 Academic Press,Inc.