Numerical Analysis

Numerical Properties of Generalized Discrepancies on Spheres of Arbitrary Dimension

Quantifying uniformity of a configuration of points on the sphere is an interesting topic that is receiving growing attention in numerical analysis. An elegant solution has been provided by Cui and Freeden [J. Cui, W. Freeden, Equidistribution on the sphere, *SIAM J. Sci. Comput.* 18 (2) (1997) 595-609], where a class of discrepancies, called generalized discrepancies and originally associated with pseudodifferential operators on the unit sphere in R3, has been introduced. The objective of this paper is to extend to the sphere of arbitrary dimension this class of discrepancies and to study their numerical properties. First we show that generalized discrepancies are diaphonies on the hypersphere. This allows us to completely characterize the sequences of points for which convergence to zero of these discrepancies takes place. Then we discuss the worst-case error of quadrature rules and we derive a result on tractability of multivariate integration on the hypersphere. At last we provide several versions of Koksma-Hlawka type inequalities for integration of functions defined on the sphere.

Comparison of quadrature rules for the Wielandt-Nyström method with statistical applications

International conference

Quadrature rules and distribution of points on manifolds

International conference

Computational aspects of discrepancies for equidistribution on the hypercube

International conference

Formule di quadratura e distribuzione di punti su varietà compatte

National conference

Quadrature rules and distribution of points on manifolds

National conference

Statistical tests of uniformity on the hypersphere

International conference

Statistical tests of uniformity on the hypersphere

International conference

Numerical and statistical properties of discrepancies on spheres

Seminar

Computing Weighted Chi-square Distributions and Related Quantities

International conference