Generalized discrepancies on the sphere
نویسندگان
چکیده
منابع مشابه
Discrepancies of Point Sequences on the Sphere and Numerical Integration
where σ denotes the normalized surface measure on Sd and f is a continuous real valued function. As a general reference on Quasi-Monte Carlo methods we mention Niederreiter [22]. The problem of distributing points on the sphere is also related to constructive multivariate approximation, see Reimer [24]. For the recent literature on spherical problems concerned with approximation and numerical i...
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When testing that a sample of n points in the unit hypercube [0, 1] comes from a uniform distribution, the Kolmogorov–Smirnov and the Cramér–von Mises statistics are simple and well-known procedures. To encompass these measures of uniformity, Hickernell introduced the so-called generalized Lp-discrepancies. These discrepancies can be used in numerical integration through Monte Carlo and quasi–M...
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Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory, but convergent if a ma...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700216