On the computation of nonnegative quadrature weights on the sphere

Applied and Computational Harmonic Analysis

Volumn 27, Issue 1, 2009, Pages 124-132

  Gräf, Manuel ^a   Kunis, Stefan ^a   Potts, Daniel ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

FFT; NFFT; Nonequispaced fast spherical Fourier transform; Quadrature; Two sphere

Indexed keywords

FFT; NFFT; NONEQUISPACED FAST SPHERICAL FOURIER TRANSFORM; QUADRATURE; TWO-SPHERE;

CONTENT BASED RETRIEVAL; FAST FOURIER TRANSFORMS;

SPHERES;

EID: 67349088427     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2008.12.003     Document Type: Article

References (18)

1. Davis P.J., and Rabinowitz P. Methods of Numerical Integration. second ed. (1984), Academic Press Inc.
2. Filbir F., and Themistoclakis W. Polynomial approximation on the sphere using scattered data. Math. Nachr. 281 (2008) 650-668
3. Freeden W., Gervens T., and Schreiner M. Constructive Approximation on the Sphere (1998), Oxford University Press, Oxford
4. Friedlander M.P. BCLS 0.1, C Software Package (2007). http://www.cs.ubc.ca/~mpf/bcls
5. Górski K.M., Hivon E., Banday A.J., Wandelt B.D., Hansen F.K., Reinecke M., and Bartelmann M. HEALPix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere. Astrophys. J. 622 (2005) 759-771
6. Habicht W., and van der Waerden B.L. Lagerung von Punkten auf der Kugel. Math. Ann. 123 (1951) 223-234
7. Hardin R.H., and Sloane N.J.A. Spherical Designs, a Library of Putatively Optimal Spherical t-Designs (2002). http://www.research.att.com/~njas/sphdesigns
8. Keiner J., Kunis S., and Potts D. NFFT 3.0, C Subroutine Library (2006). http://www.tu-chemnitz.de/~potts/nfft
9. Keiner J., Kunis S., and Potts D. Efficient reconstruction of functions on the sphere from scattered data. J. Fourier Anal. Appl. 13 (2007) 435-458
10. Keiner J., and Potts D. Fast evaluation of quadrature formulae on the sphere. Math. Comput. 77 (2008) 397-419
11. Kunis S., and Potts D. Fast spherical Fourier algorithms. J. Comput. Appl. Math. 161 (2003) 75-98
12. Q.T. Le Gia, H.N. Mhaskar, Quadrature formulas and localized linear polynomial operators on the sphere, SIAM J. Numer. Anal. (2007), in press
13. Mhaskar H.N., Narcowich F.J., and Ward J.D. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comput. 70 (2001) 1113-1130 Corrigendum on the positivity of the quadrature weights in Math. Comput. 71 (2002) 453-454
14. Nocedal J., and Wright S.J. Numerical Optimization. Springer Ser. Oper. Res. Finan. Eng. second ed. (2006), Springer, New York
15. Reimer M. Multivariate Polynomial Approximation (2003), Birkhäuser Verlag, Basel
16. Saff E.B., and Kuijlaars A.B.J. Distributing many points on a sphere. Math. Intelligencer 19 (1997) 5-11
17. Sloan I.H. Polynomial interpolation and hyperinterpolation over general regions. J. Approx. Theory 83 (1995) 238-254
18. Vanderbei R.J. Linear Programming. Internat. Ser. Oper. Res. Management Sci. third ed. vol. 114 (2008), Springer, New York Foundations and extensions