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

摘要

By means of singular value decomposition (SVD) we investigate the systems of linear algebraic equations which are derived for numerical solution of first kind Fredholm integral equations arising in two-dimensional potential theory. In order to derive a numerical ‘model’ which has the same features and peculiarities as the underlying integral equation, we apply the Galerkin method with orthonormal basis functions. The linear equations are studied with respect to (1) conditioning, (2) accuracy of the computed solution, (3) effective rank, and (4) comparison of nullspaces. As a practical example we then use our numerical method to investigate the equations of a specific geometry for which the analytical solution is not known.