Convergence Estimates For Solution Of Integral Equations With GMRES
- In this paper we derive convergence estimates for the
iterative solution of nonsymmetric linear systems by GMRES. We work
in the context of strongly convergent collectively compact sequences
of approximations to linear compact fixed point problems. Our
estimates are intended to explain the observations that the
performance of GMRES is independent of the discretization if the
resolution of the discretization is suffciently good. Our bounds are
independent of the right hand side of the equation, reflect the
r-superlinear convergence of GMRES in the infinite dimensional
setting, and also allow for more than one implementation of the
discrete scalar product. Our results are motivated by quadrature rule
approximation to second-kind Fredholm integral equations.
This research was partially supported by National Science Foundation grants
DMS-9122745 & D-9423705 (Campbell), CCR-9102853 (Ipsen), DMS-9321938 (Kelley), and
DMS-9020915 & DMS-9403224 (Meyer). Computing activity was also partially supported by an
allocation of time from the North Carolina Supercomputing Center.
- Journal of Integral Equations and Applications
- Vol 8, 1996, pp. 19-34.
- S. L. Campbell
- I. C. F. Ipsen
- C. T. Kelley
- C. D. Meyer
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