01-10 | Berichtsreihe des Mathematischen Seminars der Universität Kiel | |
Robert Plato, Gennadi Vainikko:The fast solution of periodic integral and pseudodifferential equationsby GMRESIn 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
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[Thu Feb 19 18:56:35 2009] |
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