Abstract
In this paper we consider GMRES to solve finite-dimensional approxi- mations 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.
Keywords: periodic integral equations; pseudodifferential equations; Symm’s integralequation; biharmonic equation; Cauchy integral equation; Hilbert integral equation; the hypersingular integral equation; conjugate gradient type methods; GMRES; trigonometric Galerkin method; fast solvers; complexity
Received: 2001-07-25
Revised: 2002-01-23
Accepted: 2002-02-21
Published Online: 2001
Published in Print: 2001
© Institute of Mathematics, NAS of Belarus
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