Lookup Tables, Recurrences and Complexity

The use of lookup tables can reduce the complexity of calculation of functions defined typically by mathematical recurrence relations. Although this technique has been adopted by several algebraic manipulation systems, it has not been examined critically in the literature. While the use of tabulation or “memoization” seems to be a particularly simple and worthwhile technique in some areas, there are some negative consequences. Furthermore, the expansion of this technique to other areas (other than recurrences) has not been subjected to analysis. This paper examines some of the assumptions. A more detailed technical report [9] is under preparation. This paper appeared in ACM-SIGSAM 1989 proceedings. 1 Fibonnaci Numbers: A Famous Example Consider the Fibonacci numbers, defined by a two-term recurrence

• Type: Conference
• Year: 1989
• Where: ISSAC
• Authors: Richard J. Fateman
• Keywords: Algebraic Manipulation Systems, ISSAC 1989, Mathematical Recurrence Relations, Mathematics, Worthwhile Technique