Results 1 to 10 of about 875 (151)
Gaussian quadrature rules and A-stability of Galerkin schemes for ODE
International Journal of Mathematics and Mathematical Sciences, 2003 The A-stability properties of continuous and discontinuous Galerkin methods for solving ordinary differential equations (ODEs) are established using properties of Legendre polynomials and Gaussian quadrature rules. The influence on the A-stability of the
Ali Bensebah +2 more
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Computing Gaussian quadrature rules with high relative accuracy
Numerical Algorithms, 2022 AbstractThe computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high
TERESA Laudadio +2 more
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Orthogonal polynomials and generalized Gauss-Rys quadrature formulae
Kuwait Journal of Science, 2021 Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type with respect to the even weight function $\omega^{\lambda}(t;x)=\exp(-x t^2)(1-t^2)^{\lambda-1/2}$ on $(-1,1)$, with parameters $\lambda>-1/2$ and $x>0$, are considered.
Gradimir Milovanovic, Nevena Vasovic ́
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Classical quadrature rules via Gaussian processes [PDF]
2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP), 2017 In an extension to some previous work on the topic, we show how all classical polynomial-based quadrature rules can be interpreted as Bayesian quadrature rules if the covariance kernel is selected suitably. As the resulting Bayesian quadrature rules have zero posterior integral variance, the results of this article are mostly of theoretical interest in
Särkkä, Simo, Karvonen, Toni
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The Gaussian wave packet transform via quadrature rules
IMA Journal of Numerical Analysis, 2023 Abstract We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.
Paul Bergold, Caroline Lasser
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Gaussian-type Quadrature Rules for Müntz Systems [PDF]
SIAM Journal on Scientific Computing, 2005 A method for constructing the generalized Gaussian quadrature rules for Muntz polynomials on $(0,1)$ is given. Such quadratures possess several properties of the classical Gaussian formulae (for polynomial systems), such as positivity of the weights, rapid convergence, etc. They can be applied to the wide class of functions, including smooth functions,
Gradimir V. Milovanovic +1 more
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Gaussian quadrature rules for composite highly oscillatory integrals
Mathematics of Computation, 2023 Highly oscillatory integrals of composite type arise in electronic engineering and their calculations are a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is constructed based on the classical theory of orthogonal polynomials and its nodes and weights can be computed efficiently ...
Menghan Wu, Haiyong Wang
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A numerical integration-based Kalman filter for moderately nonlinear systems
Tellus: Series A, Dynamic Meteorology and Oceanography, 2020 This paper introduces a computationally efficient data assimilation scheme based on Gaussian quadrature filtering that potentially outperforms current methods in data assimilation for moderately nonlinear systems.
Sarah A. King +2 more
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Adaptive Quadrature Schemes for Bayesian Inference via Active Learning
IEEE Access, 2020 We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules.
Fernando Llorente Fernandez +4 more
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A Note on Extended Gaussian Quadrature Rule [PDF]
Mathematics of Computation, 1976 Extended Gaussian quadrature rules of the type first considered by Kronrod are examined. For a general nonnegative weight function, simple formulas for the computation of the weights are given, together with a condition for the positivity of the weights associated with the new nodes.
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