Results 261 to 270 of about 117,411 (298)

ROUNDING-OFF ERRORS IN MATRIX PROCESSES

The Quarterly Journal of Mechanics and Applied Mathematics, 1948
A number of methods of solving sets of linear equations and inverting matrices are discussed. The theory of the rounding-off errors involved is investigated for some of the methods. In all cases examined, including the well-known 'Gauss elimination process', it is found that the errors are normally quite moderate: no exponential build-up need occur ...
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Round-off errors andp-adic numbers

Nonlinearity, 1999
Summary: We explore some connections between round-off errors in linear planar rotations and algebraic number theory. We discretize a map on a lattice in such a way as to retain invertibility, restricting the system parameter (the trace) to rational values with power-prime denominator \(p^n\).
Bosio, D., Vivaldi, F.
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Automatic propagated and round-off error analysis

Preprints of papers presented at the 13th national meeting of the Association for Computing Machinery on - ACM '58, 1958
The routine described below is a modification of the Carnegie Tech (IT) Compiler system for the IBM-650, which will provide automatic empirical analysis of propagated and round-off errors in computation. In the modified system, three kinds of variables are admissable: fixed-point integers called I-variables; floating-point numbers called C-variables ...
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Reduce Rounding Off Errors in Information Dispersal Algorithm

2019 International Conference on Computer, Control, Informatics and its Applications (IC3INA), 2019
The Information Dispersal Algorithm (IDA) is an algorithm that can be used to store files securely. Files and data packets can be broken down at the bit level into several parts and then saved to separate nodes. IDA requires a matrix generator in the form of the Vandermonde matrix and the Cauchy matrix to split and reconstruct files.
Ardhi Wijayanto, Bambang Harjito
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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.
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Round-off errors in relaxational solutions of Poisson's equation

Applied Scientific Research, 1954
Formulae 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 Richardson's extrapolation method

USSR Computational Mathematics and Mathematical Physics, 1987
The 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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An efficient stochastic method for round-off error analysis

1986
This 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 inter-experimental comparisons

Acta Crystallographica Section A Foundations of Crystallography, 1985
Two 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

1970
To 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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