ORTHPOL

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 43 articles , 2 standard articles )

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  1. Dresse, Zoé; Van Assche, Walter: Orthogonal polynomials for Minkowski’s question mark function (2015)
  2. Meurant, Gérard; Sommariva, Alvise: Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab (2014)
  3. Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto; Gervasio, Paola: Numerical mathematics (2014)
  4. Hale, Nicholas; Townsend, Alex: Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights (2013)
  5. Bilionis, Ilias; Zabaras, Nicholas: Multidimensional adaptive relevance vector machines for uncertainty quantification (2012)
  6. Mesquita, Teresa A.; Da Rocha, Z.: Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases (2012)
  7. Mastroianni, G.; Notarangelo, I.: A Nyström method for Fredholm integral equations on the real line (2011)
  8. Bultheel, Adhemar; Cruz-Barroso, Ruymán; Van Barel, Marc: On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line (2010)
  9. Gautschi, Walter: Gauss quadrature routines for two classes of logarithmic weight functions (2010)
  10. Lee, Sanghoon; Chen, Wei; Kwak, Byung Man: Robust design with arbitrary distributions using Gauss-type quadrature formula (2010)
  11. Milovanović, Gradimir V.; Cvetković, Aleksandar S.: Nonstandard Gaussian quadrature formulae based on operator values (2010)
  12. Welfert, B.D.: The weights of classical Gauss-Radau quadratures with double end-point (2010)
  13. Fermo, Luisa: A Nyström method for a class of Fredholm integral equations of the third kind on unbounded domains (2009)
  14. Xiang, Ming; Deng, Shaozhong; Cai, Wei: A sixth-order image approximation to the ionic solvent induced reaction field (2009)
  15. Milovanović, Gradimir V.; Cvetković, Aleksandar S.; Stanić, Marija P.: Trigonometric orthogonal systems and quadrature formulae (2008)
  16. Xue, Changfeng; Deng, Shaozhong: New versions of image approximations to the ionic solvent induced reaction field (2008)
  17. Cai, Wei; Deng, Shaozhong; Jacobs, Donald: Extending the fast multipole method to charges inside or outside a dielectric sphere (2007)
  18. Deng, Shaozhong; Cai, Wei: Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high-order image approximations for reaction fields (2007)
  19. Deng, Shaozhong; Cai, Wei; Jacobs, Donald: A comparable study of image approximations to the reaction field (2007)
  20. Gustafson, Sven-Åke: Some continuous programming problems in numerical analysis (2007)

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