Quadrature over the sphere

Electronic Transactions on Numerical Analysis

Volumn 20, Issue , 2005, Pages 104-118

  Atkinson, Kendall ^a   Sommariva, Alvise ^b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Euler MacLaurin expansion; Spherical integration; Trapezoidal rule

Indexed keywords

EID: 29344469815     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. M. ABRAMOWITZ AND I. STEGUN, eds., Handbook of Mathematical Functions, Dover Pub., New York, 1965.
2. K. ATKINSON, Numerical integration on the sphere, J. Australian Math. Soc., Series B, 23 (1982), pp. 332-347.
3. K. ATKINSON, An Introduction to Numerical Analysis, 2nd edition, John Wiley, New York, 1989.
4. K. ATKINSON, Quadrature of singular integrands over surfaces, Electron. Trans. Numer. Anal., 17 (2004), pp. 133-150, http://etna.mcs.kent.edu/vol.17. 2004/pp133-150.dir/pp133-150.pdf
5. D. ELLIOTT, Sigmoidal transformations and the trapezoidal rule, J. Australian Math. Soc., Series B(Electronic), 40 (1998), pp. E77-E137.
6. J. LYNESS AND B. NINHAM, Numerical quadrature and asymptotic expansions, Mathematics of Computation, 21 (1967), pp. 162-178.
7. J. LYNESS, Private communication, 2005.
8. J. LYNESS AND G. MONEGATO, The Euler-Maclaurin expansion and finite-part integrals, Numerische Mathematik, 81 (1998), pp. 273-291.
9. A. SIDI,A new variable transformation for numerical integration, in Numerical Integration IV, H. Brass and G. Häminerlin, eds., Birkhäuser Verlag, Basel, 1993, pp. 359-373.
10. A. SIDI, Practical Extrapolation Methods, Cambridge University Press, Cambridge, United Kingdom, 2003.
11. m variable transformations to numerical integration over surfaces of spheres, 2003, to appear in Journal of Computational and Applied Mathematics.
12. A. SIDI, Euler-MacLaurin expansions for integrals with endpoint singularities: A new perspective, Numerische Mathematik 98 (2004), pp. 371-387.
13. A. SIDI, Extension of a class of periodizing variable transformations for numerical integration, 2004, to appear in Mathematics of Computation.
14. 3, Numerische Mathematik, 100 (2005), pp. 519-536.
15. E. WEISSTEIN, Faá de Bruno's Formula, in MathWorld - a Wolfram Web Resource, http://mathworld.wolfram.com/FaadiBrunosFormula.html