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
europepmc +2 more sources
Roundoff error sequences in fixed-point arithmetic digital processors [PDF]
, 1976 Three assumptions are normally made about roundoff error sequences in fixed-point arithmetic digital processors: all values of error, within the limits set by the roundoff process, have an equal probability of occurrence; they are random; and they are ...
McWilliam, Andrew J.
core +6 more sources
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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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
core +2 more sources
Checking Roundoff Errors using Counterexample-Guided Narrowing [PDF]
, 2010 This paper proposes a counterexample-guided narrowing approach、which combines static analysis and testing、 to make them refine eachother. A prototype tool CANAT for checking roundoff errors betweenfloating point and fixed point numbers is reported with ...
Ogawa, Mizuhito +3 more
core +1 more source
An Introduction to Affine Arithmetic
Trends in Computational and Applied Mathematics, 2003 Affine arithmetic (AA) is a model for self-validated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal ...
J. Stolfi, L.H. de Figueiredo
doaj +1 more source
On fully discrete collocation methods for solving weakly singular integral equations
Mathematical Modelling and Analysis, 2009 A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be ...
Raul Kangro, Inga Kangro
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Nonconcurrent Error Correction in the Presence of Roundoff Noise [PDF]
Proceedings of the 45th IEEE Conference on Decision and Control, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Takos, G. +3 more
openaire +4 more sources
Round-Off Error Suppression by Statistical Averaging
AxiomsRegarding round-off errors as random is often a necessary simplification to describe their behavior. Assuming, in addition, the symmetry of their distributions, we show that one can, in unstable (ill-conditioned) computer calculations, suppress their ...
Andrej Liptaj
doaj +1 more source
Stochastic Estimation of MIMO Detection Error Caused by Low-Bitwidth QR Decomposition
IEEE Open Journal of the Communications SocietyIn this paper, we propose a new approach to justify a roundoff error impact on the accuracy of the linear least squares (LS) solution using QR decomposition.
Alexander Osinsky +4 more
doaj +1 more source