Algorithm 726: ORTHPOL—A package of routines for generating orthogonal polynomials and Gauss‐type quadrature rules. A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal polynomials. Once these are known, additional data can be generated, such as zeros of orthogonal polynomials and Gauss-type quadrature rules, for which routines are also provided. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 56 articles , 2 standard articles )

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  1. Milovanović, Gradimir V.: Symbolic-numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal $B$-spline (2017)
  2. Ahlfeld, R.; Belkouchi, B.; Montomoli, F.: SAMBA: sparse approximation of moment-based arbitrary polynomial chaos (2016)
  3. Bigoni, Daniele; Engsig-Karup, Allan P.; Eskilsson, Claes: Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs (2016)
  4. Shizgal, Bernie D.: Pseudospectral solution of the Fokker-Planck equation with equilibrium bistable states: the eigenvalue spectrum and the approach to equilibrium (2016)
  5. Baye, Daniel: The Lagrange-mesh method (2015)
  6. Dresse, Zoé; Van Assche, Walter: Orthogonal polynomials for Minkowski’s question mark function (2015)
  7. Notaris, Sotirios E.: The error norm of Gauss-Radau quadrature formulae for Bernstein-Szegö weight functions (2015)
  8. Meurant, Gérard; Sommariva, Alvise: Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab (2014)
  9. Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto; Gervasio, Paola: Numerical mathematics (2014)
  10. Deng, Shaozhong; Xue, Changfeng; Baumketner, Andriy; Jacobs, Donald; Cai, Wei: Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions (2013) ioport
  11. Hale, Nicholas; Townsend, Alex: Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights (2013)
  12. Landreman, Matt; Ernst, Darin R.: New velocity-space discretization for continuum kinetic calculations and Fokker-Planck collisions (2013)
  13. Bilionis, Ilias; Zabaras, Nicholas: Multidimensional adaptive relevance vector machines for uncertainty quantification (2012)
  14. Mesquita, Teresa A.; Da Rocha, Z.: Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases (2012)
  15. Mastroianni, G.; Notarangelo, I.: A Nyström method for Fredholm integral equations on the real line (2011)
  16. Bultheel, Adhemar; Cruz-Barroso, Ruymán; Van Barel, Marc: On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line (2010)
  17. Gautschi, Walter: Gauss quadrature routines for two classes of logarithmic weight functions (2010)
  18. Lee, Sanghoon; Chen, Wei; Kwak, Byung Man: Robust design with arbitrary distributions using Gauss-type quadrature formula (2010)
  19. Milovanović, Gradimir V.; Cvetković, Aleksandar S.: Nonstandard Gaussian quadrature formulae based on operator values (2010)
  20. Welfert, B.D.: The weights of classical Gauss-Radau quadratures with double end-point (2010)

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