Error expansions for multidimensional trapezoidal rules with Sidi transformations

Numerical Algorithms

Volumn 16, Issue 3-4, 1997, Pages 321-347

  Verlinden, P ^a   Potts, D M ^b   Lyness, J N ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF CHICAGO   (United States)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

Cubature; Euler Maclaurin expansion; Extrapolation; Multidimensional integration; Quadrature; Sidi transformation; Vertex singularity

Indexed keywords

EID: 0043234051     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019155601289     Document Type: Article

References (14)

1. F.L. Bauer, H. Rutishauser and E. Stiefel, New aspects in numerical quadrature, in: Proceedings of Symposium in Applied Mathematics, Vol. 15 (American Mathematical Society, Providence, RI, 1963) pp. 199-218.
2. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic Press, London, 1984).
3. M. Iri, S. Moriguti and Y. Takasawa, On a certain quadrature formula, Kokyuroku, Res. Inst. Sci. Kyoto 91 (1970) 82-118 (in Japanese). English translation: J. Comput. Appl. Math. 17 (1987) 3-20.
4. M. Iri, S. Moriguti and Y. Takasawa, On a certain quadrature formula, Kokyuroku, Res. Inst. Sci. Kyoto 91 (1970) 82-118 (in Japanese). English translation: J. Comput. Appl. Math. 17 (1987) 3-20.
5. N.M. Korobov, Number-Theoretic Methods of Approximate Analysis (GIFL, Moscow, 1963) (in Russian).
6. D.P. Laurie, Periodizing transformations for numerical integration, JCAM 66 (1996) 337-344.
7. J.N. Lyness and J.J. McHugh, On the remainder term in the N-dimensional Euler-Maclaurin expansion, Numer. Math. 15 (1970) 333-334.
8. J.N. Lyness, An error expansion for N-dimensional quadrature with an integrand function singular at a point, Math. Comp. 113 (1976) 1-23.
9. I. Navot, An extension of the Euler-Maclaurin summation formula to functions with a branch singularity, J. Math, and Phys. 40 (1961) 271-276.
10. W. Romberg, Vereinfachte numerische Integration, Norske Vid. Selsk. Forh. 28 (1955) 30-36.
11. T.W. Sag and G. Szekeres, Numerical evaluation of high-dimensional integrals, Math. Comp. 18 (1964) 245-253.
12. A. Sidi, A new variable transformation for numerical integration, in: Numerical Integration, Vol. 4, eds. H. Bräss and B. Hämmerlin (Birkhäuser, Basel, 1993) pp. 359-373.
13. P. Verlinden, Cubature formulas and asymptotic expansions, thesis, Katholieke Universiteit Leuven (1993).
14. P. Verlinden and A. Haegemans, An error expansion for cubature with an integrand with homoge-neous boundary singularities, Numer. Math. 65 (1993) 383-406.