A Convergent Reconstruction Method for an Elliptic Operator in Potential Form

We investigate the problem of recovering a potential q(x) in the equation −Δu + q(x)u = 0 from overspecified boundary data on the unit square in R2. The potential is characterized as a fixed point of a nonlinear operator, which is shown to be a contraction on a ball in Cα. Uniqueness of q(x) follows, as does convergence of the resulting recovery scheme. Numerical examples, demonstrating the performance of the algorithm, are presented.