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Automatic error analysis for determining precision

By Paul L. Richman

Communications of the ACM, Vol. 15 No. 9, Pages 813-817

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.

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