5 papers
Tractability of approximation in the weighted Korobov space in the worst-case setting -- a complete picture
Adrian Ebert, Friedrich Pillichshammer
In this paper, we study tractability of -approximation of one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are of product…
Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction
Adrian Ebert, Peter Kritzer, Onyekachi Osisiogu +1
We study the efficient construction of good polynomial lattice rules, which are special instances of quasi-Monte Carlo (QMC) methods. The integration rules obtained are of particul…
Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces
Adrian Ebert, Peter Kritzer, Onyekachi Osisiogu +1
We consider the efficient construction of polynomial lattice rules, which are special cases of so-called quasi-Monte Carlo (QMC) rules. These are of particular interest for the app…
Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
Adrian Ebert, Peter Kritzer, Dirk Nuyens +1
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an -dimensional integr…
Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm
Adrian Ebert, Peter Kritzer
In this paper, we study an efficient algorithm for constructing node sets of high-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh, and Sobolev spaces. The a…