Table-Based Methods

Abstract

Evaluating a function by approximating it in a rather large domain may require polynomial or rational functions of large degrees. This may lead to long delays of computation, and this may also make the numerical error control difficult. A natural way to deal with this problem is to split the interval where the function is to be approximated into several smaller subintervals. It suffices to store in a table, for each subinterval, the coefficients of a low-degree approximation that is valid in that interval. Such a method is not new (a PDP-9 implementation is reported in [7]), but it becomes very attractive nowadays, since memory is less and less expensive.