12 citations · 12 across the 10 of their papers we have counts for
13 papers
Quasi-uniform designs from random candidates: optimal candidate complexity and farthest-point sampling
Takashi Goda, Hengjun Xu
We study randomized constructions of quasi-uniform designs on a compact metric-measure space satisfying two-sided polynomial ball-growth conditions. Given integers , we fir…
Algebraic constructions of point sequences with quasi-uniform two-dimensional projections
Takashi Goda
Motivated by sequential space-filling designs for computer experiments, we study algebraic constructions of extensible point sets in the -dimensional unit cube whose two-dimensi…
Worst-case -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 with smoothness in the Lebesgue norm for…
Hidden low-discrepancy structures in random point sets
Kohei Suzuki, Takashi Goda
We study the probabilistic existence of point configurations satisfying the -net property in base within a randomly generated point set of size in the -dimens…
Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences
Takashi Goda, Roswitha Hofer, Kosuke Suzuki
In this short article, we prove that the Halton sequence, one of the most well-known low-discrepancy sequences, is not quasi-uniform in any dimension with any pairwise re…
Constructive quasi-uniform sequences over triangles
Hengjun Xu, Takashi Goda
In this paper, we develop constructive algorithms for generating quasi-uniform point sets and sequences over arbitrary two-dimensional triangular domains. Our proposed method, call…
The median trick does not help for fully nested scrambling
Takashi Goda, Kosuke Suzuki
In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scrambling are known to exhibit the same va…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part I: Lattices and Kronecker sequences
Josef Dick, Takashi Goda, Gerhard Larcher +2
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part II: digital nets and sequences
Josef Dick, Takashi Goda, Kosuke Suzuki
We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental de…
A simple universal algorithm for high-dimensional integration
Takashi Goda, David Krieg
We present a simple universal algorithm for high-dimensional integration which has the optimal error rate (independent of the dimension) in all weighted Korobov classes both in the…
Tractability results for integration in subspaces of the Wiener algebra
Josef Dick, Takashi Goda, Kosuke Suzuki
In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the -dimensional unit cube. We show that…
The Sobol' sequence is not quasi-uniform in dimension 2
Takashi Goda
Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol' sequence is not quasi-un…
A universal median quasi-Monte Carlo integration
Takashi Goda, Kosuke Suzuki, Makoto Matsumoto
We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating t…