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An efficient stochastic method for round-off error analysis
1986This paper presents a survey of research results obtained by the authors and by their team, on the round-off error propagation and the accuracy of mathematical computations.
J. Vignes, René Alt
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Round-off errors in Richardson's extrapolation method
USSR Computational Mathematics and Mathematical Physics, 1987The authors study the influence of the round-off errors on the coefficients in the Richardson extrapolation, under the assumption that these errors are of the form \(\omega h^{-1}\) or \(\omega h^{-2}\) where \(\omega\) is the mean value of a random variable.
Vilenkin, S. Ya., Kalashyan, A. N.
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Round-off errors in relaxational solutions of Poisson's equation
Applied Scientific Research, 1954Formulae are derived for estimating the magnitude of the round-off errors which arise in relaxational solutions of Poisson’s equation in one dimension and over rectangular regions. In the latter case, the number of nodes and the mesh ratio are taken as variable parameters.
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Round-off errors in inter-experimental comparisons
Acta Crystallographica Section A Foundations of Crystallography, 1985Two independent determinations of the same structure may be compared by means of statistical techniques such as normal probability plots and χ2 hypothesis tests. Computer simulations show that errors may arise in the application of these techniques if rounded estimates of structural parameters and their e.s.d.s are used in the calculations.
R. Taylor, O. Kennard
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The Increase and Cumulation of Round-Off Errors
1970To give an impression of how fast round-off errors may increase even in a not really ill-conditioned case, a short numerical example shall be discussed before reporting the results of the computer runs. The problem is to compute $${\rm{e}}\,{\rm{ = }}\,{\rm{a}}\,{\rm{ - }}\,{\rm{b}}{\rm{.c}}$$ and $${\rm{g}}\,{\rm{ = }}\,{\rm{d}}\,{\rm{ - }}\
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Finding Round-Off Error Using Symbolic Execution
2014Overflow and round-off error has been a research problem for decades. With the explosion of mobile and embedded devices, many software programs written for personal computer are now ported to run on embedded systems. The porting often requires changing floating-point numbers and operations to fixed-point ones and here round-off error between the two ...
Anh-Hoang Truong +2 more
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On round-off error in fixed-point multiplication
BIT, 1976We enumerate the round-off errors in fixed point multiplication both for rounding by chopping and for symmetric rounding. Then we compute the mean and variance of the round-off error. For symmetric rounding, the formulas differ for an odd base β vs an even base β.
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Avoiding round-off error in the Rachford–Rice equation
Fluid Phase Equilibria, 2023Markus Nielsen
exaly
Newton's method and round-off errors
Glasnik matematički, 1983Newton's method and round-off ...
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