부산대학교 도서관

In this article we present a class of iterative methods for the inverse problem of 3D acoustic scattering on a penetrable inhomogeneity. We formulate the problem as an ill-posed nonlinear operator equation in a Hilbert space. The proposed methods are based on an approximation of this equation by a strongly convex finite-dimensional variational problem. The strong convexity of the approximating problem plays the key role in a theoretical justification of our approach to numerical approximation of solutions to ill-posed problems. Specifically, this property ensures the stability of the proposed iterative methods with respect to the errors in input data as an iteration number increases. We also present results of computational experiments. [ABSTRACT FROM AUTHOR]