An SVD analysis of linear algebraic equations derived from first kind integral equations (Q1065526)

A first kind integral equation corresponding to the Dirichlet boundary problem for the Laplace equation in two space dimensions is treated by singular value decomposition. For the critical case of a vanishing singular value the variant of \textit{G. Hsiao} and \textit{R. C. MacCamy} [SIAM Rev. 15, 687-705 (1973; Zbl 0235.45006)] is recommended. For numerical approximation the Galerkin method with orthonormal basis functions (which well reflects the analytical properties) is used. The influence of the various types of errors (finite expansion, approximation of a curved boundary, numerical quadrature, finite precision computation) are thoroughly discussed, and results of numerical case studies are displayed and interpreted.