ABSTRACT
The author gives a finite difference model of the inverse problem for a certain class of elliptic partial differential equations which appear in the study of electrical impedance tomography, and shows an approximate representation of Dirichlet-to-Neumann map in terms of the coefficients of differential equation and Dirichlet data (Theorem 1.1). Using this representation, he proves that if a certain system of nonlinear algebraic equations is numerically solvable, then it is possible to reconstruct the coefficient of Calderón’s inverse problem (Theorem 1.2). His result enables to circumvent the severe instability of inverse problem by using a hybrid symbolic-numeric method (Sections 3 and 4). Some numerical examples (Examples 4.3–4.10) show that his scheme would be able to recover the deeper region of given object without the notorious resolution problem (cf. Kotre’s survey [9]).
