We investigate the problem of recovering a potential q(x) in the equation -∆u + 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 C∝. Uniqueness of q(x) follows, as does convergence of the resulting recovery scheme. Numerical examples, demonstrating the performance of the algorithm, are presented.
Copyright © 1995 Academic Press, Inc.. This article first appeared in Journal of Mathematical Analysis and Applications 195, no. 1 (1995): 44-70. doi:10.1006/jmaa.1995.1341.
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Caudill, Lester F. "A Convergent Reconstruction Method for an Elliptic Operator in Potential Form." Journal of Mathematical Analysis and Applications 195, no. 1 (1995): 44-70. doi:10.1006/jmaa.1995.1341.