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The Accuracy of Floating Point Summation
Abstract
The usual recursive summation technique is just one of several ways of computing the sum of n floating point numbers. Five summation methods and their variations are analyzed here. The accuracy of the methods is compared using rounding error analysis and numerical experiments. Four of the methods are shown to be special cases of a general class of methods, and an error analysis is given for this class. No one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases.
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Citations
Cited by
(2018) · doi:10.1109/ipdpsw.2018.00091 · Cited by 399
Ogita, T., Rump, S. M., & Oishi, S. (2005) · SIAM Journal on Scientific Computing · doi:10.1137/030601818 · Cited by 386
Accelerating the XGBoost algorithm using GPU computing
Mitchell, R., & Frank, E. (2017) · PeerJ Computer Science · doi:10.7717/peerj-cs.127 · Cited by 359
Accurately computing the log-sum-exp and softmax functions
Blanchard, P., Higham, D. J., & Higham, N. J. (2021) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/draa038 · Cited by 126
Metadata
- Authors
- Higham, N. J.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 1993-07
- Volume
- 14
- Issue
- 4
- Pages
- 783-799
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2053987390
- Cited by
- 266
- References
- 0
- FWCI
- 3.01
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Accuracy of Floating Point Summation. https://app.cochat.ai/papers/10.1137/0914050
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- Higham, N. J. (1993). The Accuracy of Floating Point Summation. SIAM Journal on Scientific Computing. https://doi.org/10.1137/0914050
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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