Simplification and optimization transformations of chains of recurrences
Eugene V. Zima · 1995
The problem of expediting the evaluation of closed-form functions at regular intervals is considered. The Chain of Recurrences technique to expedite computations is extended by rational simplifications and examined as a form of internal representation, oriented towards fast evaluation. Optimizing transformations of Chains of Recurrences are proposed. 1 Introduction A common component in the analysis and solution of many problems, is the iterative evaluation of a function G(x) over a number of points in an interval. More specifically, given a starting point x0 and an increment h, evaluation of the function G(x0 + ih) for i = 0; 1; : : : ; n occurs frequently in applications such as plotting graphs of functions, simulations, and signal processing applications. Straightforward evaluation of functions (especially obtained as the result of symbolic transformations in Computer Algebra Systems) may not be efficient. One way to speed up this process is to compute the function incrementally...