Fast Solution Of Singular Integral Equations And Correction Procedures
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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 non- sparse 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 computa- tional complexity of O(nlogn). Moreover, our method has a higher order convergence rate in Sobolev spaces with negative order than the collocation method. 1. Introduction The paper deals with the fast solution of pseudodifferential equations Au = f of order zero given on a certain curve F and is based on joint work with Di- etmar Bert hold.