Results 1 to 10 of about 175,850 (276)
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 J 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 J 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 J 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, Geoffrey Sanders
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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 ...
El-Mehdi El Arar +2 more
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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.
Rasmus Tamstorf
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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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Analysis and application of real-time compensation of positioning precision of the turntable with a harmonic function [PDF]
Metrology and Measurement Systems, 2022 In order to guarantee the accuracy of turntable angle measurement, a real-time compensation method for turntable positioning precision based on harmonic analysis is proposed in this paper.
Yi Zhou +5 more
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