Bulirsch-Stoer Algorithm

An algorithm which finds Rational Function extrapolations of the form

$$R_{i(i+1)\cdots(i+m)} = {P_\mu(x)\over P_\nu(x)} = {p_0+p_1x+\ldots+p_\mu x^\mu\over q_0+q_1x+\ldots+q_\nu x^\nu}$$

and can be used in the solution of Ordinary Differential Equations.

References

Bulirsch, R. and Stoer, J. §2.2 in Introduction to Numerical Analysis. New York: Springer-Verlag, 1991.

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.