# The Accuracy of Floating Point Summation

@article{Higham1993TheAO, title={The Accuracy of Floating Point Summation}, author={N. Higham}, journal={SIAM J. Sci. Comput.}, year={1993}, volume={14}, pages={783-799} }

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… CONTINUE READING

#### Figures, Tables, and Topics from this paper

255 Citations

Accurate floating-point summation: a new approach

- Computer Science, Mathematics
- Appl. Math. Comput.
- 2007

5- PDF

A New Distillation Algorithm for Floating-Point Summation

- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 2005

21 Highly Influenced- PDF

A Distillation Algorithm for Floating-Point Summation

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 1999

30- PDF

One solution of the accurate summation using fixed-point accumulator

- Mathematics
- 2015 23rd Telecommunications Forum Telfor (TELFOR)
- 2015

1

Fast and Accurate Floating Point Summation with Application to Computational Geometry

- Mathematics, Computer Science
- Numerical Algorithms
- 2004

26

Accurate and Efficient Floating Point Summation

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2004

76

#### References

SHOWING 1-10 OF 85 REFERENCES

Floating-point computation of functions with maximum accuracy

- Mathematics, Computer Science
- 1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)
- 1975

42

Floating-Point Computation of Functions with Maximum Accuracy

- Mathematics, Computer Science
- IEEE Transactions on Computers
- 1977

27

The accurate solution of certain continuous problems using only single precision arithmetic

- Mathematics
- 1985

8

A floating-point technique for extending the available precision

- Computer Science, Mathematics
- 1970

473- PDF