The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Accurate Sum and Dot Product
Abstract
Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, $K\ge 3$. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.
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Cites
The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
Taussky, O., & Knuth, D. E. (1970) · The American Mathematical Monthly · doi:10.2307/2317055 · Cited by 3,822
Accuracy and Stability of Numerical Algorithms: Second Edition
Higham, N. J. (2002) · doi:10.1137/1.9780898718027 · Cited by 3,803
Accuracy and stability of numerical algorithms
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The art of computer programming. Vol.2: Seminumerical algorithms
Knuth, D. E. (1981) · Virtual Defense Library (Ministerio de Defensa) · Cited by 1,232
IEEE Standard for Binary Floating Point Arithmetic
Ieee, A. (1985) · Medical Entomology and Zoology · Cited by 886
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates
Shewchuk, J. R. (1997) · Discrete & Computational Geometry · doi:10.1007/pl00009321 · Cited by 569
Calmet, J. (1982) · Cited by 328
The Accuracy of Floating Point Summation
Higham, N. J. (1993) · SIAM Journal on Scientific Computing · doi:10.1137/0914050 · Cited by 266
Design, implementation and testing of extended and mixed precision BLAS
Li, X. S., Demmel, J. W., Bailey, D. H., Henry, G., Hida, Y., Iskandar, J., Kahan, W., Kang, S. Y., Kapur, A., Martin, M. C., et al. (2002) · ACM Transactions on Mathematical Software · doi:10.1145/567806.567808 · Cited by 226
Grabmeier, J., Kaltofen, E., & Weispfenning, V. (2003) · Springer eBooks · doi:10.1007/978-3-642-55826-9 · Cited by 165
Metadata
- Authors
- Ogita, T., Rump, S. M., & Oishi, S.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2005-01
- Volume
- 26
- Issue
- 6
- Pages
- 1955-1988
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W1968165559
- Cited by
- 386
- References
- 14
- FWCI
- 21.02
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ogita, T., Rump, S. M., & Oishi, S. (2005). Accurate Sum and Dot Product. SIAM Journal on Scientific Computing. https://doi.org/10.1137/030601818
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
