A stochastic roundoff error analysis for the convolution [PDF]
Mathematics of Computation, 1992 We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication.
Daniela Calvetti
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Degeneracy in the presence of roundoff errors [PDF]
Linear Algebra and its Applications, 1988 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Fletcher, Fletcher, R.
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Certified Roundoff Error Bounds Using Semidefinite Programming [PDF]
ACM Transactions on Mathematical Software, 2017 Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations.
Victor Magron +2 more
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Fast and Accurate GPU-Accelerated Computation of Two-Electron Four-Center Coulomb Repulsion Integrals. [PDF]
J Comput ChemOur GPU software rapidly and accurately computes two‐electron, four‐center Coulomb repulsion integrals using Slater‐type orbitals. It involves applying a simple transformation to eliminate the Coulomb singularity and using the trapezoidal quadrature rule. The quadrature rule converges rapidly, as demonstrated in this graph.
Kaur A +7 more
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Implementation of affine arithmetic using floating-point arithmetic: how to handle roundoff errors
, 2014 International audienceAffine arithmetic is one of the extensions of interval arithmetic, which aimsat counteracting the variable dependency problem.
Ninin, Jordan, Revol, Nathalie
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Optimum structures of digital controllers in sampled-data systems: a roundoff noise analysis [PDF]
, 2002 In this paper, the effect of roundoff noise in a digital controller is analyzed for a sampled-data system in which the digital controller is implemented in a state-space realization. A new measure, called averaged roundoff noise gain, is derived.
J. Wu +7 more
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Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations [PDF]
, 2021 We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally ...
Constantinides, G +3 more
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Axioms, 2023 This paper is presented in the context of sensitivity analysis (SA) of large-scale data assimilation (DA) models. We studied consistency, convergence, stability and roundoff error propagation of the reduced-space optimization technique arising in ...
Luisa D’Amore, Rosalba Cacciapuoti
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Reducing roundoff errors in numerical integration of planetary ephemeris [PDF]
, 2023 Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data).
Pavlov, Dmitry +2 more
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Estimación del error en cierta clase de métodos numéricos combinados de estrategia recorrectora
Revista de Matemática: Teoría y Aplicaciones, 2009 This paper shows an analysis of the order for the approximation and roundoff errors in combined numerical scheme with recorrector strategy of Adams–Moulton– Bashfort family.
Aymée Marrero, Marta Lourdes Baguer
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