Generalized discrepancies are a class of discrepancies introduced in the seminal paper [1] to measure uniformity of points over the unit sphere in R3. However, convergence to 0 of this quantity has been shown only in the case of spherical t−designs. In the following, we completely characterize sequences for which convergence to 0 of D(PN;A) holds. The interest of this result is that, when evaluating uniformity on the sphere, generalized discrepancies are much simpler to compute than the well-known spherical cap discrepancy.

Generalized Discrepancies on the Sphere

SERI, RAFFAELLO;
2007-01-01

Abstract

Generalized discrepancies are a class of discrepancies introduced in the seminal paper [1] to measure uniformity of points over the unit sphere in R3. However, convergence to 0 of this quantity has been shown only in the case of spherical t−designs. In the following, we completely characterize sequences for which convergence to 0 of D(PN;A) holds. The interest of this result is that, when evaluating uniformity on the sphere, generalized discrepancies are much simpler to compute than the well-known spherical cap discrepancy.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/5274
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