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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