Safety in numbers: The boundless errors of numerical computation

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Abstract
Perhaps the greatest unresolved question in numerical computing is how to cope with the issue of uncertainty in the accuracy of computed numerical quantities. The problem is not so much the errors in the answers, but the lack of a correct error bound or a confidence interval. The problem arises because of the failure to keep track of known errors and because of unknown errors due to finite sampling techniques. Several approaches to this question are discussed, principally interval analysis and probabilistic techniques. Reasons for the neglect of the uncertainty issue are suggested, and the benefits of providing consistently correct answers are considered. 13 refs.

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