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 65 articles , 2 standard articles )

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  1. Notaris, Sotirios E.: Anti-Gaussian quadrature formulae based on the zeros of Stieltjes polynomials (2018)
  2. Vabishchevich, Petr N.: Numerical solution of time-dependent problems with fractional power elliptic operator (2018)
  3. Deckers, Karl; Mougaida, Ahlem; Belhadjsalah, Hédi: Algorithm 973: Extended rational Fejér quadrature rules based on Chebyshev orthogonal rational functions (2017)
  4. Milovanović, Gradimir V.: Symbolic-numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal $B$-spline (2017)
  5. Ahlfeld, R.; Belkouchi, B.; Montomoli, F.: SAMBA: sparse approximation of moment-based arbitrary polynomial chaos (2016)
  6. Bigoni, Daniele; Engsig-Karup, Allan P.; Eskilsson, Claes: Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs (2016)
  7. Shizgal, Bernie D.: Pseudospectral solution of the Fokker-Planck equation with equilibrium bistable states: the eigenvalue spectrum and the approach to equilibrium (2016)
  8. Babaei, Masoud; Alkhatib, Ali; Pan, Indranil: Robust optimization of subsurface flow using polynomial chaos and response surface surrogates (2015)
  9. Baye, Daniel: The Lagrange-mesh method (2015)
  10. Dresse, Zoé; Van Assche, Walter: Orthogonal polynomials for Minkowski’s question mark function (2015)
  11. Notaris, Sotirios E.: The error norm of Gauss-Radau quadrature formulae for Bernstein-Szegö weight functions (2015)
  12. Mahendra Verma; Mario Suarez: DixonTest.CriticalValues: A Computer Code to Calculate Critical Values for the Dixon Statistical Data Treatment Approach (2014)
  13. Meurant, Gérard; Sommariva, Alvise: Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab (2014)
  14. Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto; Gervasio, Paola: Numerical mathematics (2014)
  15. 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
  16. Hale, Nicholas; Townsend, Alex: Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights (2013)
  17. Landreman, Matt; Ernst, Darin R.: New velocity-space discretization for continuum kinetic calculations and Fokker-Planck collisions (2013)
  18. Bilionis, Ilias; Zabaras, Nicholas: Multidimensional adaptive relevance vector machines for uncertainty quantification (2012)
  19. Mesquita, Teresa A.; Da Rocha, Z.: Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases (2012)
  20. Mastroianni, G.; Notarangelo, I.: A Nyström method for Fredholm integral equations on the real line (2011)

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