Bibliography for Gauss-Kronrod Quadrature

unabridged

 

  1. Stieltjes Polynomials and Gauss-Kronrod Quadrature for Jacobi Weight Functions
    Peherstorfer, F.; Petras, K.
    Numerische Mathematik, 2003, vol. 95, no. 4, pp. 689-706, Ingenta.  
  2. Asymptotics for Stieltjes polynomials, Padé-type approximants, and Gauss-Kronrod quadrature.  
    Bello Hernández, M.; de la Calle Ysern, B.; Guadalupe Hernández, J. J.; Lopez Lagomasino, G.
    J. Anal. Math.  86  (2002), 1--23, MathSciNet.  
  3. Self-validating Gauss-Kronrod quadrature
    Adam, G.; Adam, S.; Papp, E.
    Romanian Journal of Physics, 2001, vol. 46, no. 5/6, pp. 313-330, Ingenta.  
  4. Increasing reliability of Gauss-Kronrod quadrature by Eratosthenes' sieve method
    Adam, Gh. ; Adam, S.  
    Computer Physics Communications, v 135, n 3, Apr 15, 2001, p 261-277, Compendex.
  5. Stopping functionals for Gaussian quadrature formulas
    Ehrich, Sven
    Journal of Computational and Applied Mathematics, v 127, n 1-2, Jan, 2001, p 153-171, Compendex.
  6. Weighted convergence of Lagrange interpolation based on Gauss-Kronrod nodes.
    Ehrich, Sven; Mastroianni, Giuseppe
    J. Comput. Anal. Appl. 2 (2000), no. 2, 129--157, MathSciNet.  
  7. Ultraspherical Gauss-Kronrod quadrature is not possible for lambda >3
    Peherstorfer, Franz; Petras, Knut  
    SIAM Journal on Numerical Analysis, v 37, n 3, 2000, p 927-948, Compendex.
  8. Computation of Gauss-Kronrod quadrature rules.
    Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L.
    Math. Comp. 69 (2000), no. 231, 1035--1052, MathSciNet.  
  9. Computation of Gauss-Kronrod quadrature rules with non-positive weights.
    Ammar, G. S.; Calvetti, D.; Reichel, L.
    Electron. Trans. Numer. Anal. 9 (1999), 26--38 (electronic), MathSciNet.  
  10. Positivity of Gauss-Kronrod formulae for a certain ultraspherical weight function.
    Petras, Knut
    Applications and computation of orthogonal polynomials (Oberwolfach, 1998), 195--202, Internat. Ser. Numer. Math., 131, Birkhäuser, Basel, 1999, MathSciNet.  
  11. Stieltjes polynomials and the error of Gauss-Kronrod quadrature formulas.
    Ehrich, Sven
    Applications and computation of orthogonal polynomials (Oberwolfach, 1998), 57--77, Internat. Ser. Numer. Math., 131, Birkhäuser, Basel, 1999, MathSciNet.  
  12. On Product Integration with Gauss-Kronrod Nodes.
    Ehrich, Sven
    Siam journal on numerical analysis, 1998, vol. 35, no. 1, pp. 78, Ingenta.  
  13. Calculation of Gauss-Kronrod Quadrature Rules  
    Dirk P. Laurie  
    Mathematics of Computation, Vol. 66, No. 219. (Jul., 1997), pp. 1133-1145, Jstor.  
  14. Mathematica implementation of double adaptive quadrature
    Favati, P.; Fiorentino, G.; Lotti, G.; Romani, F.  
    Proceedings of the International Mathematica Symposium, Innovations in Mathematics, 1997, p 145-151, Compendex.
  15. High order error constants of Gauss-Kronrod quadrature formulas.
    Ehrich, Sven
    Analysis, 1996, vol. 16, no. 4, pp. 335--345, Ingenta.  
  16. Note on Peano constants of Gauss-Kronrod quadrature schemes
    Ehrich, Sven
    Journal of Computational and Applied Mathematics, v 66, n 1-2, Jan 31, 1996, p 177-183, Compendex.
  17. Practical error estimates for the Gauss-Kronrod quadrature formula.
    Ehrich, Sven
    Numerical methods and error bounds (Oldenburg, 1995), 74--79, Math. Res., 89, Akademie Verlag, Berlin, 1996, MathSciNet.  
  18. Asymptotic Properties of Stieltjes Polynomials and Gauss-Kronrod Quadrature Formulae.
    Ehrich, Sven
    Journal of approximation theory, 1995, vol. 82, no. 2, pp. 287-303, Ingenta.  
  19. Stieltjes polynomials and Gauss-Kronrod quadrature formulae for measures induced by Chebyshev polynomials.
    Notaris, Sotirios E.
    Special functions (Torino, 1993). Numer. Algorithms 10 (1995), no. 1-2, 167--186, MathSciNet.  
  20. Error Bounds for Gauss-Kronrod Quadrature Formulae  
    Sven Ehrich  
    Mathematics of Computation, Vol. 62, No. 205. (Jan., 1994), pp. 295-304, Jstor.  
  21. Gauss-Kronrod formulas
    Lecture Notes in Computer Science, n 848, 1994, p 78, Compendex.
  22. Error bounds for Gauss-Kronrod quadrature formulae of analytic functions.
    Notaris, S. E.
    Numerische mathematik, 1993, vol. 64, no. 3, pp. 371, Ingenta.  
  23. Complex Gauss-Kronrod integration rules for certain Cauchy principal value integrals.
    Caliò, F.; Marchetti, E.
    Computing 50 (1993), no. 2, 165--173, MathSciNet.  
  24. An overview of results on the existence or nonexistence and the error term of Gauss-Kronrod quadrature formulae.
    Notaris, Sotirios E.
    Approximation and computation (West Lafayette, IN, 1993), 485--496, Internat. Ser. Numer. Math., 119, Birkhäuser Boston, Boston, MA, 1994, MathSciNet.  
  25. On Gauss-Kronrod Quadrature Formulae of Chebyshev Type  
    Sotirios E. Notaris  
    Mathematics of Computation, Vol. 58, No. 198. (Apr., 1992), pp. 745-753, Jstor.  
  26. On zeros of complex polynomials related to particular Gauss-Kronrod quadrature formulas.  
    Caliò, F.; Marchetti, E.
    Facta Univ. Ser. Math. Inform.  No. 7 (1992), 49--57, MathSciNet.  
  27. On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas.
    Peherstorfer, Franz
    J. Approx. Theory 70 (1992), no. 2, 156--190, MathSciNet.  
  28. Einige neue Ergebnisse zu den Fehlerkonstanten der Gauß-Kronrod-Quadraturformel. (German)
    Ehrich, S.
    [Recent results on the error constants for the Gauss-Konrad quadrature formula]
    Bericht über die Wissenschaftliche Jahrestagung der GAMM (Leipzig, 1992). Z. Angew. Math. Mech. 73 (1993), no. 7-8, T882--T886, MathSciNet.  
  29. Some new formulae for the Stieltjes polynomials relative to classical weight functions
    Notaris, Sotirios E.
    SIAM Journal on Numerical Analysis, v 28, n 4, Aug, 1991, p 1196-1206, Compendex.
  30. Gauss - kronrod integration rules with general weight function
    Yong, Jiang  
    Huadong Gongxueyuan Xuebao, n 4, 1991, p 32, Compendex.
  31. Algorithm 691: Improving QUADPACK automatic integration routines
    Favati, Paola; Lotti, Grazia; Romani, Francesco  
    ACM Transactions on Mathematical Software, v 17, n 2, Jun, 1991, p 218-232, Compendex.
  32. On Stieltjes Polynomials and Gauss-Kronrod Quadrature  
    Franz Peherstorfer  
    Mathematics of Computation, Vol. 55, No. 192. (Oct., 1990), pp. 649-664, Jstor.  
  33. Empirical Mathematics: the First Patterson Extension of Gauss-Kronrod Rules.
    Rabinowitz, Philip; Elhay, Sylvan; Kautsky, Jaroslav
    International journal of computer mathematics, 1990, vol. 36, no. 1/2, pp. 119, Ingenta.  
  34. Gauss-Kronrod quadrature formulae for weight functions of Bernstein-szego type, II
    Notaris, Sotirios E.
    Journal of Computational and Applied Mathematics, v 29, n 2, Feb 15, 1990, p 161-169, Compendex.
  35. Erratum to: "Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type"
    Gautschi, W.; Notaris, S. E.
    J. Comput. Appl. Math. 27 (1989), no. 3, 429, MathSciNet.  
  36. Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type.
    Gautschi, Walter; Notaris, Sotorios E.
    J. Comput. Appl. Math. 25 (1989), no. 2, 199--224, MathSciNet.  
  37. A Family of Gauss-Kronrod Quadrature Formulae  
    Walter Gautschi, Theodore J. Rivlin  
    Mathematics of Computation, Vol. 51, No. 184. (Oct., 1988), pp. 749-754, Jstor.  
  38. An Algebraic Study of Gauss-Kronrod Quadrature Formulae for Jacobi Weight Functions  
    Walter Gautschi, Sotirios E. Notaris  
    Mathematics of Computation, Vol. 51, No. 183. (Jul., 1988), pp. 231-248, Jstor.  
  39. Corrigenda: "Gauss-Kronrod integration rules for Cauchy principal value integrals"
    Rabinowitz, Philip
    Math. Comp. 50 (1988), no. 182, 655, MathSciNet.  
  40. Gauss-Kronrod quadrature---a survey.
    Gautschi, Walter
    Numerical methods and approximation theory, III (Ni\v s, 1987), 39--66, Univ. Nis, Nis, 1988, MathSciNet.  
  41. Newton's method and Gauss-Kronrod quadrature.
    Gautschi, Walter; Notaris, Sotirios E.
    Numerical integration, III (Oberwolfach, 1987), 60--71, Internat. Schriftenreihe Numer. Math., 85, Birkhäuser, Basel, 1988, MathSciNet.  
  42. On Computing Gauss-Kronrod Quadrature Formulae  
    Franca Calio, Walter Gautschi, Elena Marchetti  
    Mathematics of Computation, Vol. 47, No. 176. (Oct., 1986), pp. 639-650, Jstor.  
  43. Supplement to On Computing Gauss-Kronrod Quadrature Formulae  
    Franca Calio, Walter Gautschi, Elena Marchetti  
    Mathematics of Computation, Vol. 47, No. 176. (Oct., 1986), pp. S57-S63, Jstor.  
  44. On the Definiteness of Gauss-Kronrod Integration Rules  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 225-227, Jstor.  
  45. A stable Gauss-Kronrod algorithm for Cauchy principal-value integrals.
    Rabinowitz, P.
    Computers & Mathematics with Applications, v 12B, n 5-6, Sep-Dec, 1986, p 1249-1254, Compendex.
  46. Correction: "Gauss-Kronrod integration rules for Cauchy principal value integrals"
    Rabinowitz, Philip
    Math. Comp. 45 (1985), no. 171, 277, MathSciNet.  
  47. Gauss-Kronrod Integration Rules for Cauchy Principal Value Integrals  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 41, No. 163. (Jul., 1983), pp. 63-78, Jstor.  
  48. The Exact Degree of Precision of Generalized Gauss-Kronrod Integration Rules  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1275-1283, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004