RIGOROUS ERROR ANALYSIS OF NUMERICAL ALGORITHMS VIA SYMBOLIC COMPUTATIONS

We present a symbolic technique of error analysis of numerical algorit hms, which acts as a preprocessor to the actual numerical computation. The technique provides rigorous, a priori bounds which are universal for inputs in a prescribed domain. The method is an alternative to int erval arithmetic in applications where speed and rigor but not necessa rily the tight bounds are the main concerns. The technique was invente d to perform the computer-assisted proof of chaos in the Lorenz equati ons. (C) 1996 Academic Press Limited.