An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes

Numerical Algorithms

Volumn 45, Issue 1-4, 2007, Pages 101-112

  Hasegawa, Takemitsu ^a   Hibino, Susumu ^a   Hosoda, Yohsuke ^a   Ninomiya, Ichizo ^a  

^a UNIVERSITY OF FUKUI   (Japan)

Author keywords

Adaptive algorithm; Automatic quadrature; Numerical comparison

Indexed keywords

EID: 35348814346     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-007-9090-6     Document Type: Article

References (16)

1. Berntsen, J., Espelid, T.O.: Error estimation in automatic quadrature routines. ACM Trans. Math. Softw. 17, 233-252 (1991)
2. Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration, 2nd edn. Academic, Orlando, FL (1984)
3. Favati, P., Fiorentino, G., Lotti, G., Romani, F.: Local error estimates and regularity tests for the implementation of double adaptive quadrature. ACM Trans. Math. Softw. 23, 16-31 (1997)
4. Favati, P., Lotti, G., Romani, F.: Interpolatory integration formulas for optimal composition. ACM Trans. Math. Softw. 17, 207-217 (1991)
5. Favati, P., Lotti, G., Romani, F.: ALGORITHM 691 Improving QUADPACK automatic integration routines. ACM Trans. Math. Softw. 17, 218-232 (1991)
6. Favati, P., Lotti, G., Romani, F.: Theoretical and practical efficiency measures for symmetric interpolatory quadrature formulas. BIT 34, 546-557 (1994)
7. Favati, P., Di Marco, G., Lotti, G., Romani, F.: Asymptotic behavior of automatic quadrature. J. Complex. 10, 296-340 (1994)
8. Gander, W., Gautschi, W.: Adaptive quadrature - revisited. BIT 40, 84-101 (2000)
9. Kahaner, D.K.: Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229-259. Academic, Orlando, FL (1971)
10. Ninomiya, I.: Improvement of adaptive Newton-Cotes quadrature methods. J. Inf. Process. 3, 162-170 (1980)
11. Oliver, J.: A practical strategy for the Clenshaw-Curtis quadrature method. J. Inst. Math. Appl. 8, 53-56 (1971)
12. Oliver, J.: A doubly-adaptive Clenshaw-Curtis quadrature method. Comput. J. 15, 141-147 (1972)
13. Piessens, R., de Doncker-Kapenga, E., Überhuber, C.W., Kahaner, D.K.: QUADPACK, A Subroutine Package for Automatic Integration. Springer, Berlin (1983)
14. Plaskota, L., Wasilkowski, G.W.: Adaption allows efficient integration of functions with unknown singularities. Numer. Math. 102, 123-144 (2005)
15. Sugiura, H., Sakurai, T.: On the construction of high-order integration formulae for the adaptive quadrature method. J. Comput. Appl. Math. 28, 367-381 (1989)
16. Venter, A., Laurie, D.P.: A doubly adaptive integration algorithm using stratified rules. BIT 42, 183-193 (2002)