01-10   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Robert Plato, Gennadi Vainikko:

The fast solution of periodic integral and pseudodifferential equationsby GMRES

In this paper we consider GMRES to solve finite-dimensional approximations of a class of well-posed linear operator equations in Hilbert spaces. It is shown that the speed of convergence is superlinear. As a consequence we have that GMRES can be used as a fast solver of a fully discrete variant of the trigonometric Galerkin equations associated with periodic integral equations.

Mathematics Subject Classification (1991): 31A30; 35J05; 42A05; 42A15; 45E05; 45E10; 65F10; 65F25; 65R20; 65N38; 65T40; 65Y20

Keywords: periodic integral equations, pseudodifferential equations, Symm's integral equation, biharmonic equation, Cauchy integral equation, Hilbert integral equation, hypersingular integral equation, conjugate gradient type methods, GMRES, trigonometric Galerkin method, fast solvers, complexity


Mail an Jens Burmeister
[Thu Feb 19 18:56:35 2009]
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