Results 21 to 30 of about 73,280 (293)
Modeling round-off errors in hydrodynamic simulations [PDF]
, 2021 International audienceThe growth of the computing capacities makes it possible to obtain more and more precise simulation results. These results are often calculated in binary64 with the idea that round-off errors are not significant.
Weens, William +2 more
core
Improved Modular Division Implementation with the Akushsky Core Function
Computation, 2022 The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex.
Mikhail Babenko +2 more
doaj +1 more source
Enhancing single precision with quasi-double precision: achieving double-precision accuracy in the Model for Prediction Across Scales – Atmosphere (MPAS-A) version 8.2.1 [PDF]
Geoscientific Model DevelopmentThe limitations of high-performance computing (HPC) significantly constrain the development of numerical models. Traditional numerical models often employ double precision to ensure result accuracy, but this comes at a high computational cost.
J. Lai +6 more
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A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations [PDF]
, 2017 We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretization errors with a new term ...
Kehlet, B. +6 more
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Ain Shams Engineering Journal, 2014 In this article, we present homotopy perturbation method, adomian decomposition method and differential transform method to obtain a closed form solution of the (1 + n)-dimensional Burgers’ equation.
Vineet K. Srivastava, Mukesh K. Awasthi
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A Note on the Perturbation of arithmetic expressions
مجلة بغداد للعلوم, 2016 In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is ...
Baghdad Science Journal
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Numerical integration of the Cauchy problem with non-singular special points
Discrete and Continuous Models and Applied Computational Science, 2023 Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics.
Aleksandr A. Belov, Igor V. Gorbov
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A quantitative probabilistic investigation into the accumulation of rounding errors in numerical ODE solution. [PDF]
, 2009 We examine numerical rounding errors of some deterministic solvers for systems of ordinary differential equations (ODEs) from a probabilistic viewpoint. We show that the accumulation of rounding errors results in a solution which is inherently random and
Turner, Amanda G. +2 more
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Relative distance—an error measure in round-off error analysis [PDF]
Mathematics of Computation, 1982 Olver ( SIAM J. Numer. Anal. , v. 15, 1978, pp. 368-393) suggested relative precision as an attractive substitute for relative error in round-off error analysis. He remarked that in certain respects the error measure
openaire +1 more source
Journal of Applied Mathematics, 2013 We propose a new iterative method to find the bisymmetric minimum norm solution of a pair of consistent matrix equations A1XB1=C1, A2XB2=C2. The algorithm can obtain the bisymmetric solution with minimum Frobenius norm in finite iteration steps in the ...
Aijing Liu +2 more
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