Termination Criteria for Linear Problems

We study two termination criteria which are used in computational practice. They are analyzed for linear problems in the average case setting. It is assumed that arbitrary continuous linear functionals can be computed and consecutive approximations are chosen in the best possible way. The first termination criterion is satisfied if the difference between two consecutive approximations becomes less than a certain bound τ. We prove that the first termination criterion gives satisfactory results only for some cases. The second termination criterion is satisfied if two consecutive differences between consecutive approximations become less than τ. We prove that the second termination criterion gives satisfactory results for all cases.