Istituto di Scienza e Tecnologie dell'Informazione     
Romani F. On the implementation of approximating algorithms. Internal note IEI-B84-03, 1984.
Let g(x) be a function and let f(x,l) be a set of approximations to g(x). Assume the truncator error to have a series expansion in l and the roundoff error to grow as a power of l^-1. This situation arises frequently in Numerical Analysis, e.g. for the approximation of derivates and integrals, in solving differential equatins and in calculatin bilinear forms. In this work, implementation strategies fr algorithms of this kind are discussed, taking into account the behaviour of roundoff error, the use of interpolation and/or multiple precision arithmetic and the possible knowledge of the constants involved in the error bounds. The main result is that the behaviour of the error introduced by interpolation in independent of the functions f and g and the values of l, thus allowing a general discussion of the optimal choices.

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