Fast Solution Of Singular Integral EquationsAnd Correction Procedures

The paper deals with the fast solution of pseudodifferential equations Au = f on a curve F arising, for example, from a boundary value problem. The usual approximation methods produce always unstructurized and nonsparse coefficient matrices. Thus, we need in general O(n?) operations (or O(n?) operations if we use multigrid strategies) for calculating n unknowns of the approximate solution. Here we present a method having a computational complexity of O(nlogn). Moreover, our method has a higher order convergence rate in Sobolev spaces with negative order than the collocation method.