FastGaussQuadrature

FastGaussQuadrature.jl: A Julia package to compute n-point Gauss quadrature nodes and weights to 16-digit accuracy and in O(n) time. So far the package includes gausschebyshev(), gausslegendre(), gaussjacobi(), gaussradau(), gausslobatto(), gausslaguerre(), and gausshermite(). This package is heavily influenced by Chebfun.

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References in zbMATH (referenced in 33 articles )

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  1. Aceto, Lidia; Novati, Paolo: Padé-type approximations to the resolvent of fractional powers of operators (2020)
  2. Aceto, Lidia; Novati, Paolo: Rational approximations to fractional powers of self-adjoint positive operators (2019)
  3. Gil, Amparo; Segura, Javier; Temme, Nico M.: Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures (2019)
  4. Gil, Amparo; Segura, Javier; Temme, Nico M.: Noniterative computation of Gauss-Jacobi quadrature (2019)
  5. Aceto, Lidia; Novati, Paolo: Efficient implementation of rational approximations to fractional differential operators (2018)
  6. Acosta, Gabriel; Borthagaray, Juan Pablo; Bruno, Oscar; Maas, Martín: Regularity theory and high order numerical methods for the (1D)-fractional Laplacian (2018)
  7. Bremer, James: On the numerical solution of second order ordinary differential equations in the high-frequency regime (2018)
  8. Saadatmandi, Abbas; Khani, Ali; Azizi, Mohammad-Reza: A sinc-Gauss-Jacobi collocation method for solving Volterra’s population growth model with fractional order (2018)
  9. Bremer, James: On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations (2017)
  10. Bremer, James; Rokhlin, Vladimir: On the nonoscillatory phase function for Legendre’s differential equation (2017)
  11. Brzeziński, Dariusz W.: Comparison of fractional order derivatives computational accuracy -- right hand vs left hand definition (2017)
  12. Elgindy, Kareem T.: High-order, stable, and efficient pseudospectral method using barycentric Gegenbauer quadratures (2017)
  13. Jahanshahi, S.; Babolian, E.; Torres, D. F. M.; Vahidi, A. R.: A fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives (2017)
  14. Kleefeld, A.; Reichwein, E.: Improvement of the inside-outside duality method (2017)
  15. Pearson, John W.; Olver, Sheehan; Porter, Mason A.: Numerical methods for the computation of the confluent and Gauss hypergeometric functions (2017)
  16. Rutka, Przemysław; Smarzewski, Ryszard: Explicit barycentric formulae for osculatory interpolation at roots of classical orthogonal polynomials (2017)
  17. Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Paschoa, Vanessa G.: Approximate calculation of sums. II: Gaussian type quadrature (2016)
  18. Briggs, J. P.; Pennycook, S. J.; Fergusson, J. R.; Jäykkä, J.; Shellard, E. P. S.: Separable projection integrals for higher-order correlators of the cosmic microwave sky: acceleration by factors exceeding 100 (2016)
  19. Brzeziński, Dariush W.: Accuracy problems of numerical calculation of fractional order derivatives and integrals applying the Riemann-Liouville/Caputo formulas (2016)
  20. Deaño, Alfredo; Huybrechs, Daan; Opsomer, Peter: Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials (2016)

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