Sources of error in computation

20. R. P. Brent, Sources of error in computation, in Error, Approximation and Accuracy (edited by F. R. de Hoog and C. L. Jarvis), University of Queensland Press, Brisbane, 1973, 122-128. MR 52#2124, 54#9069.

Paper: pdf (201K).


In the numerical approximation or prediction of a physical situtation, errors may arise in the following ways:

Although model and truncation errors are extremely important, they are not the subject of this paper, which considers data and rounding errors.

With numerically unstable methods rounding errors may be amplified by "catastrophic cancellation". With numerically stable methods this can not occur, but many small errors may accumulate. The amount of accumulation depends on the number system used, and different number systems are compared.


This is a brief, expository paper on the subject of computational errors, with examples drawn from Brent [17], Forsythe ["Pitfalls in computation, or why a Math Book isn't enough", American Math. Monthly 77 (1970), 931-956], and Wilkinson [ Rounding errors in algebraic processes, Prentice-Hall, 1963].

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