Results 1 to 10 of about 23,597 (146)
Stochastic rounding: implementation, error analysis and applications [PDF]
Royal Society Open Science, 2022 Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to x.
Matteo Croci +4 more
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Stochastic Rounding and Its Probabilistic Backward Error Analysis [PDF]
SIAM Journal of Scientific Computing, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas Higham, Theo Mary
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Probabilistic Rounding Error Analysis of Householder QR Factorization [PDF]
SIAM Journal on Matrix Analysis and Applications, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicholas Higham
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A New Approach to Probabilistic Rounding Error Analysis [PDF]
SIAM 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
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Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms [PDF]
SIAM Journal of Scientific Computing, 2021 31 pages including references, 3 ...
Alyson Fox
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Rounding-Error Analysis of Multigrid \({V}\)-Cycles
SIAM Journal of Scientific ComputingThis paper provides a rounding-error analysis for two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic and focuses on a two-grid scheme that is perturbed on the coarse grid to allow for an approximate coarse-grid solve.
Stephen Mccormick, Rasmus Tamstorf
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Probabilistic Error Analysis of Limited-Precision Stochastic Rounding
SIAM Journal of Scientific ComputingClassical 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 O(nu), where n is the problem size and u is ...
Mantas Mikaitis +2 more
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Error Analysis of Sum-Product Algorithms under Stochastic Rounding
SIAM Journal of Scientific ComputingThe quality of numerical computations can be measured through their forward error, for which finding good error bounds is challenging in general. For several algorithms and using stochastic rounding (SR), probabilistic analysis has been shown to be an effective alternative for obtaining tight error bounds.
Eric Petit, El-Mehdi El Arar
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Design and Implementation of Multithreaded Reproducible DGEMV for Phytium Processor [PDF]
Jisuanji kexue, 2022 In high-performance computing,the accumulation of rounding error in the process of solving the large-scale,long time and ill-conditioned problem will lead to invalidated results.These results are useful for the developers to debug programs and check ...
CHEN Lei, TANG Tao, QI Hai-jun, JIANG Hao, HE Kang
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Sensors, 2022 Multi-robot motion and observation generally have nonlinear characteristics; in response to the problem that the existing extended Kalman filter (EKF) algorithm used in robot position estimation only considers first-order expansion and ignores the higher-
Miao Wang, Weifeng Liu, Chenglin Wen
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