Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm

In this paper we consider algorithms to compute bounds of the A-norm of the error in the preconditioned conjugate gradient (PCG) algorithm. We extend to PCG formulas that were given in an earlier paper 8]. We give numerical experiments which show that good upper and lower bounds can be obtained provided estimates of the lowest and largest eigenvalues of the preconditioned matrix are given or adaptively computed. This revised version was published online in August 2006 with corrections to the Cover Date.