Ill-conditioned matrices in the scattering of waves from hard corrugated surfaces

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Abstract
In this paper we present an analysis of the conditioning character of the matrices obtained in the different methods for solving the integral equations that appear in the scattering of waves from a hard corrugated surface. It is found that the matrices derived from the Rayleigh hypothesis become ill conditioned for large corrugations when the approach is not valid at any rate. The method based on the extinction theorem developed by Masel, Merrill, and Miller is analytically correct, but it becomes ill conditioned and no practical numerical solutions can be obtained for large values of the corrugation strength, depending on the precision of the computer used. Finally the self-consistent method with the numerical procedure developed by Garcia and Cabrera is well conditioned and leads always to a good practical numerical solution for all kinds of corrugations, no matter how large.