Bibliography for Gauss-Kronrod Quadrature

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  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. 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.
  4. 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.  
  5. 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.  
  6. On Product Integration with Gauss-Kronrod Nodes.
    Ehrich, Sven
    Siam journal on numerical analysis, 1998, vol. 35, no. 1, pp. 78, Ingenta.  
  7. Calculation of Gauss-Kronrod Quadrature Rules  
    Dirk P. Laurie  
    Mathematics of Computation, Vol. 66, No. 219. (Jul., 1997), pp. 1133-1145, Jstor.  
  8. 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.
  9. 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.
  10. 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.  
  11. Error Bounds for Gauss-Kronrod Quadrature Formulae  
    Sven Ehrich  
    Mathematics of Computation, Vol. 62, No. 205. (Jan., 1994), pp. 295-304, Jstor.  
  12. Gauss-Kronrod formulas
    Lecture Notes in Computer Science, n 848, 1994, p 78, Compendex.
  13. Complex Gauss-Kronrod integration rules for certain Cauchy principal value integrals.
    Caliò, F.; Marchetti, E.
    Computing 50 (1993), no. 2, 165--173, MathSciNet.  
  14. On Gauss-Kronrod Quadrature Formulae of Chebyshev Type  
    Sotirios E. Notaris  
    Mathematics of Computation, Vol. 58, No. 198. (Apr., 1992), pp. 745-753, Jstor.  
  15. 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.
  16. On Stieltjes Polynomials and Gauss-Kronrod Quadrature  
    Franz Peherstorfer  
    Mathematics of Computation, Vol. 55, No. 192. (Oct., 1990), pp. 649-664, Jstor.  
  17. 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.  
  18. 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.  
  19. 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.  
  20. 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.  
  21. 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.  
  22. 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.  
  23. On the Definiteness of Gauss-Kronrod Integration Rules  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 225-227, Jstor.  
  24. Gauss-Kronrod Integration Rules for Cauchy Principal Value Integrals  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 41, No. 163. (Jul., 1983), pp. 63-78, Jstor.  
  25. 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