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Erratum: Comparison of Epidemiological Estimates for 19 Cancer Types Using Electronic Health Record Databases in England: An Analysis of CPRD Aurum and CPRD GOLD Databases with Linked Hospital Episode Statistics and Cancer Registry Data [Corrigendum]. [PDF]
Clin Epidemioleuropepmc +1 more source
Stochastic Rounding and Its Probabilistic Backward Error Analysis [PDF]
SIAM Journal of Scientific Computing, 2021 Stochastic rounding rounds a real number to the next larger or smaller floating-point number with probabilities 1 minus the relative distances to those numbers. It is gaining attention in deep learning because it can increase the success of low precision computations.
Nicholas Higham, Theo Mary
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A New Approach to Probabilistic Rounding Error Analysis [PDF]
SIAM Journal of Scientific Computing, 2019 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
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Probabilistic Error Analysis of Limited-Precision Stochastic Rounding [PDF]
SIAM Journal of Scientific ComputingAbstract. Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear algebra algorithms, one can prove probabilistic error bounds that grow as [Formula: see ...
Mantas Mikaitis +2 more
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Rounding error analysis of Horner's scheme
Computing, 1983In this paper we establish a forward error analysis of the generalized complete Horner scheme for a polynomial $$p = \sum {a_j X^{n - j} } $$ with pivotal pointsz 1, ...,z n .
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Statistical Analysis of the Roundness Error Data
Advanced Materials Research, 2012In order to simulate the actual roundness measurement accurately, must find the mathematical model of the actual roundness data, the paper’s main emphasis is doing statistical analysis by plenty of measurement data of roundness, using mathematical knowledge to prove that the actual characteristics of roundness parameters obey the normal distribution ...
Zhao Peng Dong +3 more
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Rounding Error Analysis of Interval Algorithms
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1984AbstractUsing 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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