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ADCM
2004
74views more  ADCM 2004»
13 years 4 months ago
Extremal Systems of Points and Numerical Integration on the Sphere
This paper considers extremal systems of points on the unit sphere Sr Rr+1, related problems of numerical integration and geometrical properties of extremal systems. Extremal sys...
Ian H. Sloan, Robert S. Womersley
NA
2008
78views more  NA 2008»
13 years 4 months ago
A walk through energy, discrepancy, numerical integration and group invariant measures on measurable subsets of euclidean space
(A) The celebrated Gaussian quadrature formula on finite intervals tells us that the Gauss nodes are the zeros of the unique solution of an extremal problem. We announce recent re...
S. B. Damelin
SIAMNUM
2010
120views more  SIAMNUM 2010»
12 years 11 months ago
Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere
A set XN of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree at most t over XN is equal to the average value of the polynomial o...
Congpei An, Xiaojun Chen, Ian H. Sloan, Robert S. ...
IPPS
2003
IEEE
13 years 9 months ago
Partitioning with Space-Filling Curves on the Cubed-Sphere
Numerical methods for solving the systems of partial differential equations arising in geophysical fluid dynamics rely on a variety of spatial discretization schemes (e.g. finit...
John M. Dennis
ADCM
2008
187views more  ADCM 2008»
13 years 4 months ago
Approximation on the sphere using radial basis functions plus polynomials
In this paper we analyse a hybrid approximation of functions on the sphere S2 R3 by radial basis functions combined with polynomials, with the radial basis functions assumed to be...
Ian H. Sloan, Alvise Sommariva