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, Volume 49, Issue 4, pp 363–372 | Cite as

Two algorithms for the construction of product formulas

  • Annamaria Palamara Orsi
Article
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Abstract

By using formulas already known in the literature, we present two algorithms, together with their Fortran implementations, for the numerical construction of product quadrature rules.

AMS (MOS) Subject Classifications

65D32 

Key words

Product quadrature rules algorithms 

Zwei Algorithmen für die numerische Konstruktion von Produkt-Quadraturformeln

Zusammenfassung

Mit Hilfe von in der Literatur bekannten Formeln geben wir zwei Algorithmen und ihre Fortran-Implementierung für die numerische Konstruktion von Produkt-Quadraturformeln.

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References

  1. [1]
    Atkinson, K.: The numerical solution of Fredholm integral equations of the second kind. SIAM J. Numer. Anal.4, 337–348 (1967).Google Scholar
  2. [2]
    Baker, C. T. H.: The numerical treatment of integral equations. Oxford: Clarendon Press 1977.Google Scholar
  3. [3]
    Baratella, P., Moroni, P.: Asymptotic error bounds of product formulas for functions with interior singularity. Rapporto interno29, Dpt. di Matematica, Politecnico di Torino (1990).Google Scholar
  4. [4]
    Criscuolo, G., Mastroianni, G., Monegato, G.: Convergence properties of a class of product formulas for weakly singular integral equations. Math. Comput.55, 213–230 (1990).Google Scholar
  5. [5]
    Delves, L. M., Walsh, J. (ed.): Numerical solution of integral equations. Oxford: Clarendon Press 1974.Google Scholar
  6. [6]
    Monegato, G.: Stieltjes polynomials and related quadrature rules. SIAM Review24, 137–158 (1982).Google Scholar
  7. [7]
    Monegato, G.: Orthogonal polynomials and product integration for one-dimensional Fredholm integral equations with “nasty” kernels. In: Kuhnert, F., Silbermann, B. (eds.) Problems and methods in mathematical physics, 185–192. Leipzig: B. G. Teubner Verlagsgesellschaft, 1989 (9. TMP, Teubner-Texte zur Mathematik, Band 111).Google Scholar
  8. [8]
    Monegato, G., Palamara Orsi, A.: Product formulas for Fredholm integral equations with rational kernel functions. Proceedings on the Oberwolfach Conference on Numerical Integration, ISNM85, 140–156. Basel: Birkhäuser 1988.Google Scholar
  9. [9]
    Palamara Orsi, A.: Metodo di integrazione prodotto per la risoluzione numerica di equazioni integrali di Volterra di seconda specie con nucleo debolmente singolare. Rapporto interno6, Dpt. di Matematica, Politecnico di Torino (1990).Google Scholar
  10. [10]
    Phillips, J. L.: The use of collocation as a projection method for solving linear operator equations. SIAM J. Numer. Anal.9, 14–28 (1972).Google Scholar
  11. [11]
    Piessens, R.: Modified Chenshaw-Curtis integration and applications to numerical computation of integral transforms. In: Numerical integration, Nato ASI Series, Series C203 Dordrecht: Reidel P. C. 1987.Google Scholar
  12. [12]
    Sloan, I. H., Smith, W. E.: Product integration with the Clenshaw-Curtis points. Implementation and error estimates. Numer. Math.34, 387–401 (1980).Google Scholar
  13. [13]
    Sloan, I. H., Smith, W. E.: Properties of interpolatory product integration rules. SIAM J. Numer. Anal.19, 427–442 (1982).Google Scholar
  14. [14]
    Smith, W. E., Sloan, I. H.: Product integration rules based on the zeros of Jacobi polynomials. SIAM J. Numer. Anal.17, 1–13 (1980).Google Scholar
  15. [15]
    Szegö, G.: Über gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfunktion gehören. Math. Ann.110, 501–513 (1934).Google Scholar
  16. [16]
    Szegö, G.: Orthogonal polynomials. (Amer. Math. Soc. Publ., 23). Providence, R.I.: A.M.S. 1975.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Annamaria Palamara Orsi
    • 1
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly

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