Josef Dick

activity

20112026

S^{2}

with small spherical cap discrepancy

36 citations · 36 across the 8 of their papers we have counts for

collaborators

Showing 2026 · math.NAShow all

4 papers · 2 filters

math.NA2026

The curse of dimensionality for geometric $L_{1}$ -discrepancies with nonnegative weights

Josef Dick

We prove that the normalized star, extreme, and periodic $L_{1}$ -discrepancies with arbitrary nonnegative weights suffer from the curse of dimensionality. A single elementary lemma i…

math.NA2026

Spherical Cap $L_{2}$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant

Johann S. Brauchart, Josef Dick, Friedrich Pillichshammer

We prove that the information complexity (i.e., the inverse) of the classical spherical cap $L_{2}$ discrepancy on the $d$ -dimensional sphere $S^{d}$ decreases with dimension…

math.NA2026

Worst-case $L_{p}$ -approximation of periodic functions using median lattice algorithms

Zexin Pan, Mou Cai, Josef Dick +2

We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space $H_{d, α, γ}$ with smoothness $α > 1/2$ in the Lebesgue norm $L_{p} ([0, 1]^{d})$ for…

math.NA2026

The inverse of the star discrepancy of a union of randomly shifted Korobov rank-1 lattice point sets depends polynomially on the dimension

Jiarui Du, Josef Dick

The inverse of the star discrepancy, $N (ε, s)$ , defined as the minimum number of points required to achieve a star discrepancy of at most $ε$ in dimension $s$ , is known to depend l…

The curse of dimensionality for geometric L1​-discrepancies with nonnegative weights

Spherical Cap L2​ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant

Worst-case Lp​-approximation of periodic functions using median lattice algorithms

The inverse of the star discrepancy of a union of randomly shifted Korobov rank-1 lattice point sets depends polynomially on the dimension

The curse of dimensionality for geometric $L_{1}$ -discrepancies with nonnegative weights

Spherical Cap $L_{2}$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant

Worst-case $L_{p}$ -approximation of periodic functions using median lattice algorithms