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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 ...
Philippe Langlois
exaly   +3 more sources

A New Approach to Probabilistic Rounding Error Analysis [PDF]

open access: yesSIAM Journal of Scientific Computing, 2019
Summary: Traditional rounding error analysis in numerical linear algebra leads to backward error bounds involving the constant \(\gamma_n = nu/(1-nu)\), for a problem size \(n\) and unit roundoff \(u\). In light of large-scale and possibly low-precision computations, such bounds can struggle to provide any useful information.
Nicholas Higham, Theo Mary
exaly   +4 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
openaire   +2 more sources

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