Results 11 to 20 of about 1,238 (176)
Generalized eigenvalue methods for Gaussian quadrature rules [PDF]
Annales Henri Lebesgue, 2020 A quadrature rule of a measure μ on the real line represents a conic combination of finitely many evaluations at points, called nodes, that agrees with integration against μ
Blekherman, Grigoriy +4 more
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Anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges’ sense
, 2022 Abstract
Petrovic, Nevena +2 more
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MathematicsGaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure dσ^. It is important to be able to estimate the quadrature error in the Gaussian rule used.
Dušan Lj. Djukić +5 more
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Set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense
, 2022 Anti-Gaussian quadrature rules, introduced by Laurie in [1], have the property that their error is equal in magnitude but of the opposite sign to the corresponding Gaussian quadrature rules. Guided by that idea, we define and analyse the set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense (see [2]), with ...
Petrovic, Nevena
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On the Computation of Gaussian Quadrature Rules for Chebyshev Sets of Linearly Independent Functions
SIAM Journal on Numerical Analysis, 2022 We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in the sense that $2l$ basis functions can be integrated exactly with just $l$ points and weights.
Huybrechs, Daan
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Computation of Generalized Averaged Gaussian Quadrature Rules [PDF]
, 2022 The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing.
Spalević, Miodrag
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Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation [PDF]
, 2009 A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of ...
Lombardi, Guido
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Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval [PDF]
, 2014 We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian ...
Deaño Cabrera, Alfredo, Deaño, Alfredo
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Gaussian quadrature rules with exponential weights on (−1, 1)
Numerische Mathematik, 2011 The main goal of the paper is to apply Gaussian quadrature rules based on the zeros of Pollaczek-type polynomials to the Lagrange interpolation process and to prove the convergence of a Nyström method. The authors give a quadrature rule that requires a lower computational cost and converges with the order of the best polynomial approximation.
Maria Carmela De Bonis +2 more
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Numerical Integration in S-PLUS or R: A Survey
Journal of Statistical Software, 2003 This paper reviews current quadrature methods for approximate calculation of integrals within S-Plus or R. Starting with the general framework, Gaussian quadrature will be discussed first, followed by adaptive rules and Monte Carlo methods.
Diego Kuonen
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