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Rigorous Error Analysis of Numerical Algorithms via Symbolic Computations

M. Mrozek
Journal / Anthology

Journal of Symbolic Computation
Year: 1996
Volume: 22
Page range: 435-458

We present a symbolic technique of error analysis of numerical algorithms, 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 interval arithmetic in applications where speed and rigor but not necessarily the tight bounds are the main concerns. The technique was invented to perform the computer-assisted proof of chaos in the Lorenz equations.

*Applied Mathematics > Numerical Methods