Error Bounds and Stopping Rules for Extrapolation Methods

In this paper, we present two different types of error boundsfor the approximation of functions by extrapolation methods(also called elimination methods). First, we give some a prioritype bounds; by means of these, one can, before starting theextrapolation process, estimate the errors of the extrapolatedvalues. Next, we present the so-called stopping rules; thesecan be used to decide during the process if the desired accuracyhas already been reached. Using the same techniques as for deducingthe error bounds, we then give criteria which help to predictthe form of the resulting error curves. It turns out that theseare in many cases monotone functions. Finally, two numericalexamples illustrate the results of this paper.