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CADNA: a library for estimating round-off error propagation

Computer Physics Communications, 2008
The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed.
Jézéquel, Fabienne, Chesneaux, Jean-Marie   +1 more
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Round-off errors in variational calculations

Journal of Computational Physics, 1968
Abstract Rigorous bounds are derived for the effect of round-off errors in variational calculations for eigenvalues of linear operators. These bounds are simple to compute. They are used to derive an alternative variation principle which minimizes the effect of round-off errors. A numerical example of the use of the techniques is given.
L M Delves
exaly   +3 more sources

Balancing truncation and round-off errors in FEM: One-dimensional analysis

Journal of Computational and Applied Mathematics, 2021
In finite element methods, the accuracy of the solution cannot increase indefinitely since the round-off error related to limited computer precision increases when the number of degrees of freedom (DoFs) is large enough.
Matthias Möller, Henk M Schuttelaars
exaly   +2 more sources

Round-off error in products

Computing, 1975
LetA 1 andA 2 be floating point numbers represented in arbitrary base β and randomly chosen from a logarithmic distribution. Letr denote the round-off error $$r = fl(A_1 * A_2 ) - (A_1 * A_2 )$$ where * is floating point multiplication and wherefl(A 1*A 2 ...
Richard Goodman, Alan Feldstein
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Mean and variance of round off error

Signal Processing, 2016
Gadzhiev [4] derived expressions for round off error mean and round off error variance when the rounded variable follows the centered uniform and centered Gaussian distributions. Here, we derive general expressions for round off error mean and round off error variance when the rounded variable is any continuous random variable on the real line or any ...
Rui Li, Saralees Nadarajah
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Round-Off Errors

, 2015
Bo Einarsson
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Complexity Estimates Depending on Condition and Round-off Error

Journal of the ACM, 1998
This paper has two agendas. One is to develop the foundations of round-off in computation. The other is to describe an algorithm for deciding feasibility for polynomial systems of equations and inequalities together with its complexity analysis and its round-off properties. Each role reinforces the other.
Felipe Cucker, Steve Smale
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Accumulation of Round-Off Error in Fast Fourier Transforms

Journal of the ACM, 1970
The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients.
Toyohisa Kaneko, Bede Liu
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A Round-Off Error Model with Applications to Arithmetic Expressions

SIAM Journal on Computing, 1979
An arithmetic expression is evaluated in a form most suitable to a given computing structure. To select this “suitable form” restructuring algorithms using laws of associativity, commutativity, and distributivity have been proposed. This raises the question of how different ways of evaluating an expression influence the propagation of errors due to ...
Vijay B. Aggarwal, James W. Burgmeier
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On Round-Off Errors in Linear Programming

1970
exaly   +2 more sources