計算機計算における累績丸め誤差の推定

概要

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A simple method is proposed to estimate the accumulated round-off error in computer computation. The error may come from the complicated interaction between values that are to be numerically processed, such as added/subtracted and multiplied/divided. Severe relative error occurs, for example, when a number is subtracted from one of almost equal value. A set of formulae can estimate satisfactorily the limit as well as the standard deviation of errors, and the latter plays a central role in indicating an approximated (absolute) mean value of randomly distributed errors. The effectiveness of the algorithm is demonstrated by treating an example which contains a very complicated numerical processing of power series, such as addition/subtraction, division, development and reversion. Special formulae, which avoid problems of computer over/underflow, are proposed to estimate the standard deviation.
一般社団法人日本機械学会の論文
1991-01-25