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The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the
step size). The function can then be fitted and evaluated at 
to yield very accurate results. Press et al. (1992)
describe this process as turning lead into gold. Richardson extrapolation is one of the key ideas used in the
popular and robust Bulirsch-Stoer Algorithm of solving Ordinary Differential Equations.
See also Bulirsch-Stoer Algorithm
References
Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer.,
p. 106, 1990.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Richardson Extrapolation and the Bulirsch-Stoer Method.'' §16.4 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 718-725, 1992.