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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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Rounding errors in autoregressive processes

International Journal of Forecasting, 1993
Abstract Time series observations are often rounded, but are modelled as though they were continuous and no rounding had occurred. This paper examines the impact of rounding on the estimation of parameters in autoregressive time series models, deriving appropriate adjustments for the estimates of the true parameters when using rounded data ...
Antonie Stam, Kenneth O. Cogger
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Computational Graphs and Rounding Error

SIAM Journal on Numerical Analysis, 1974
Using graphs for representing computational processes, relative error propagation is described. It is shown how this relates to the condition of a problem and to the property of a process to be benign, i.e., to have only harmless effects of rounding errors. In particular, composition of processes is studied under these aspects.
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Automatic Linear Correction of Rounding Errors

BIT Numerical Mathematics, 2001
The standard analysis of the effect of rounding errors in floating point arithmetic is based on the estimation of computed value \(fl(.)\) with respect to the elementary errors bounded by the so-called epsilon machine. A first order approximation of the global rounding error accumulating elementary rounding errors is obtained using some numerical ...
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Rounding Error Analysis of Interval Algorithms

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1984
AbstractUsing the linearization method, a rounding error analysis of interval algorithms is established. It is shown that the interval midpoints and radii are approximate solutions of real evaluation algorithms and of certain linear systems uniquely associated to each interval algorithm.
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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 ...
Goodman, Richard, Feldstein, Alan
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