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- Gaussian_quadrature abstract "In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.(See numerical integration for more on quadrature rules.)An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the points xi and weights wi for i = 1,...,n.The domain of integration for such a rule is conventionally taken as [−1, 1], so the rule is stated asGaussian quadrature as above will only produce accurate results if the function f(x) is well approximated by a polynomial function within the range [−1,1]. The method is not, for example, suitable for functions with singularities. However, if the integrated function can be written as, where is approximately polynomial and is known, then alternative weights and points that depend on the weighting function may give better results, whereCommon weighting functions include(Chebyshev–Gauss) and (Gauss–Hermite).It can be shown (see Press, et al., or Stoer and Bulirsch) that the evaluation points xi are just the roots of a polynomial belonging to a class of orthogonal polynomials.".
- Gaussian_quadrature thumbnail Legendrepolynomials6.svg?width=300.
- Gaussian_quadrature wikiPageExternalLink PRIMUS_KHATTRI.pdf.
- Gaussian_quadrature wikiPageExternalLink index.html?pg=179.
- Gaussian_quadrature wikiPageExternalLink GaussianQuadrature.
- Gaussian_quadrature wikiPageExternalLink gauss_quadrature.html.
- Gaussian_quadrature wikiPageExternalLink arbitrary_weight_rule.html.
- Gaussian_quadrature wikiPageExternalLink legendre-gauss.html.
- Gaussian_quadrature wikiPageExternalLink gq.
- Gaussian_quadrature wikiPageExternalLink gsl.
- Gaussian_quadrature wikiPageID "50579".
- Gaussian_quadrature wikiPageRevisionID "605887143".
- Gaussian_quadrature first "Nico M.".
- Gaussian_quadrature hasPhotoCollection Gaussian_quadrature.
- Gaussian_quadrature id "3.5".
- Gaussian_quadrature id "Legendre-GaussQuadrature".
- Gaussian_quadrature id "p/g043510".
- Gaussian_quadrature last "Temme".
- Gaussian_quadrature title "Gauss quadrature formula".
- Gaussian_quadrature title "Legendre-Gauss Quadrature".
- Gaussian_quadrature title "§3.5: Gauss Quadrature".
- Gaussian_quadrature subject Category:Numerical_integration_(quadrature).
- Gaussian_quadrature comment "In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.(See numerical integration for more on quadrature rules.)An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the points xi and weights wi for i = 1,...,n.The domain of integration for such a rule is conventionally taken as [−1, 1], so the rule is stated asGaussian quadrature as above will only produce accurate results if the function f(x) is well approximated by a polynomial function within the range [−1,1]. ".
- Gaussian_quadrature label "Cuadratura de Gauss".
- Gaussian_quadrature label "Gaussian quadrature".
- Gaussian_quadrature label "Gauß-Quadratur".
- Gaussian_quadrature label "Kwadratury Gaussa".
- Gaussian_quadrature label "Kwadratuurformule van Gauss".
- Gaussian_quadrature label "Méthodes de quadrature de Gauss".
- Gaussian_quadrature label "Quadratura di Gauss".
- Gaussian_quadrature label "Regra de quadratura gaussiana".
- Gaussian_quadrature label "Метод Гаусса (численное интегрирование)".
- Gaussian_quadrature label "ガウス求積".
- Gaussian_quadrature label "高斯求积".
- Gaussian_quadrature sameAs Gaussovo_kvadraturní_pravidlo.
- Gaussian_quadrature sameAs Gauß-Quadratur.
- Gaussian_quadrature sameAs Cuadratura_de_Gauss.
- Gaussian_quadrature sameAs Méthodes_de_quadrature_de_Gauss.
- Gaussian_quadrature sameAs Quadratura_di_Gauss.
- Gaussian_quadrature sameAs ガウス求積.
- Gaussian_quadrature sameAs Kwadratuurformule_van_Gauss.
- Gaussian_quadrature sameAs Kwadratury_Gaussa.
- Gaussian_quadrature sameAs Regra_de_quadratura_gaussiana.
- Gaussian_quadrature sameAs m.0dck6.
- Gaussian_quadrature sameAs Q767680.
- Gaussian_quadrature sameAs Q767680.
- Gaussian_quadrature wasDerivedFrom Gaussian_quadrature?oldid=605887143.
- Gaussian_quadrature depiction Legendrepolynomials6.svg.
- Gaussian_quadrature isPrimaryTopicOf Gaussian_quadrature.
