Abstract
The loss of accuracy incurred in adding a small, accurate quantity to a larger one, using floating point addition, can be avoided by keeping account of a small correction to the sum. This is particularly valuable in machines which perform truncation, but no proper round-off, following arithmetic operations. In the first part of the article the details of the method are discussed. In the second part the effectiveness of the method is shown in an application to the step-by-step integration of ordinary differential equations.
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References
S. Gill,A process for the step-by-step integration of differential equations on an automatic digital computing machine, Proc. Cambr. Ph. Soc. vol. 47 1951, pp. 96–108.
M. J. Romanelli,Runge-Kutta methods for the solution of ordinary differential equations, Ralston and Wilf, Mathematical Methods for Digital Computers 1959, chap. 9, p. 115.
J. M. Wolfe,Reducing truncation errors by programming, ACM vol.7/6 june 1964 p. 355.
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Møller, O. Quasi double-precision in floating point addition. BIT 5, 37–50 (1965). https://doi.org/10.1007/BF01975722
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DOI: https://doi.org/10.1007/BF01975722