Convergence Estimates For Solution Of Integral Equations With GMRES

ABSTRACT

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

Journal of Integral Equations and Applications

Vol 8, 1996, pp. 19-34.

CO-AUTHORS

S. L. Campbell

I. C. F. Ipsen

C. T. Kelley

C. D. Meyer

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