Convergence Estimates for Solution of Integral Equations with Gmres
نویسندگان
چکیده
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 xed 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 su ciently good. Our bounds are independent of the right hand side of the equation, re ect the r-superlinear convergence of GMRES in the in nite 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.
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