ERROR ANALYSIS OF RICHARDSON’S EXTRAPOLATIONS

We propose estimators of a round off error contained in an approximation for Richardson’s extrapolation scheme under finite digit arithmetic. We also propose a stopping criterion, based on consideration of the round off error, for Richardson’s extrapolation scheme with respect to risk technical systems (automobile and railway transport, aircrafts, marine and river transport, chemical installations, munitions, information society suffering by terrorism). Usually the error of an approximation is evaluated by a truncation error. However, we can accurately estimate the behavior of this error utilizing both truncation and round off errors under finite digit arithmetic.