Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators

A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765.