Adaptive quadrature - Revisited

BIT Numerical Mathematics

Volumn 40, Issue 1, 2000, Pages 84-101

  Gander, Walter ^a   Gautschi, Walter ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Adaptive quadrature; Gauss quadrature; Kronrod rules

Indexed keywords

EID: 0037823843     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022318402393     Document Type: Article

References (12)

1. Carl de Boor, On writing an automatic integration algorithm, in Mathematical Software, John R. Rice ed., Academic Press, New York, 1971, pp. 201-209.
2. Philip J. Davis and Philip Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, Orlando, 1984.
3. Walter Gander, A simple adaptive quadrature algorithm, Research Report No. 83-03, Seminar für Angewandte Mathematik, ETH, Zürich, 1993.
4. Walter Gander, Computermathematik, Birkhäuser, Basel, 1992.
5. Walter Gander and Walter Gautschi, Adaptive quadrature - revisited, Research Report #306, Institut für Wissenschaftliches Rechnen, ETH, Zürich, 1998.
6. S. Garribba, L. Quartapelle, and G. Reina, Algorithm 36 - SNIFF: Efficient selftuning algorithm for numerical integration, Computing, 20 (1978), pp. 363-375.
7. Walter Gautschi, Gauss-Kronrod quadrature - a survey, in Numerical Methods and Approximation Theory III, G. V. Milovanović, ed., Faculty of Electronic Engineering, University of Niš, Niš, 1988, pp. 39-66.
8. Walter Gautschi, Numerical Analysis: An Introduction, Birkhäuser, Boston, 1997.
9. Michael T. Heath, Scientific Computing, McGraw-Hill, New York, 1997.
10. William M. Kahan, Handheld calculator evaluates integrals, Hewlett-Packard Journal 31:8 (1980), pp. 23-32.
11. David K. Kahaner, Comparison of numerical quadrature formulas, in Mathematical Software, John R. Rice ed., Academic Press, New York, 1971, pp. 229-259.
12. J. N. Lyness, Notes on the adaptive Simpson quadrature routine, J. Assoc. Comput. Mach., 16 (1969), pp. 483-495.