Computing a Subinterval of the Image
Journal of the ACM (JACM)
A precise numerical analysis program
Communications of the ACM
Variable-precision exponentiation
Communications of the ACM
LISP-based "big-float" system is not slow
ACM SIGSAM Bulletin
Automatically adapting programs for mixed-precision floating-point computation
Proceedings of the 27th international ACM conference on International conference on supercomputing
Hi-index | 48.25 |
The problem considered is that of evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision floating-point arithmetic operations. For example, the expression might be &pgr;/(&pgr; + 1/2 - e) √2), which is rational in the data &pgr;, e, √2. An automatic error analysis technique is given for determining, directly from the results of a trial low-precision interval arithmetic calculation, just how much precision and data accuracy are required to achieve a desired final accuracy. The techniques given generalize easily to the evaluation of many nonrational expressions.