15 citations · 163 across the 28 of their papers we have counts for
32 papers
Asymptotically optimal bracketing covers for anchored boxes with applications to star discrepancy
Kosuke Suzuki
Bracketing covers and -covers provide finite discretizations of the anchored boxes that define the star discrepancy. Let and denote the corresponding brac…
Bounded independence for the inverse star discrepancy
Kosuke Suzuki
We give a random-bit-efficient construction for the inverse star discrepancy. For every fixed , -wise independent uniform points $\boldsymbol{X}_1,\ldots,\boldsymbol{…
Separation properties of scrambled digital nets and related random point sets
Kosuke Suzuki
We study how standard randomization procedures affect the local geometry of quasi-Monte Carlo point sets, as measured by their minimum distance and mesh ratio. Although probabilist…
Making the RANMAR pseudorandom number generator in LAMMPS up to four times faster, with an implementation of jump-ahead
Hiroshi Haramoto, Kosuke Suzuki
Massively parallel molecular simulations require pseudorandom number streams that are provably non-overlapping and reproducible across thousands of compute units in parallel comput…
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…
Coarse scrambling for Sobol' and Niederreiter sequences
Kosuke Suzuki
We introduce coarse scrambling, a novel randomization for digital sequences that permutes blocks of digits in a mixed-radix representation. This construction is designed to preserv…
Exact -separation radius of Sobol' sequences in dimension 2
Kosuke Suzuki
Quasi-uniformity is a fundamental geometric property of point sets, crucial for applications such as kernel interpolation, Gaussian process regression, and space-filling experiment…
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…
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…
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…
Improved bounds on the gain coefficients for digital nets in prime power base
Takashi Goda, Kosuke Suzuki
We study randomized quasi-Monte Carlo integration by scrambled nets. The scrambled net quadrature has long gained its popularity because it is an unbiased estimator of the true int…
Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate
Josef Dick, Takashi Goda, Kosuke Suzuki
We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ul…
Recent advances in higher order quasi-Monte Carlo methods
Takashi Goda, Kosuke Suzuki
In this article we review some of recent results on higher order quasi-Monte Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally introduced the concept…
Characterization of digital -nets and digital -sequences in base
Roswitha Hofer, Kosuke Suzuki
We give a characterization of all matrices which generate a -net in base and a characterization of all matrices $B,C\in\mathbb{…
Characterization of matrices such that generates a digital net with -value zero
Hiroki Kajiura, Makoto Matsumoto, Kosuke Suzuki
We study -dimensional digital nets over generated by matrices where is the identity matrix and is a square matrix. We give a characterization…
Digital net properties of a polynomial analogue of Frolov's construction
Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki +2
Frolov's cubature formula on the unit hypercube has been considered important since it attains an optimal rate of convergence for various function spaces. Its integration nodes are…
Lattice rules in non-periodic subspaces of Sobolev spaces
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
We investigate quasi-Monte Carlo (QMC) integration over the -dimensional unit cube based on rank-1 lattice point sets in weighted non-periodic Sobolev spaces $\mathcal{H}(K_{α,\…
Quasi-Monte Carlo integration for twice differentiable functions over a triangle
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
We study quasi-Monte Carlo integration for twice differentiable functions defined over a triangle. We provide an explicit construction of infinite sequences of points including one…
Enumeration of the Chebyshev-Frolov lattice points in axis-parallel boxes
Kosuke Suzuki, Takehito Yoshiki
For a positive integer , the -dimensional Chebyshev-Frolov lattice is the -lattice in generated by the Vandermonde matrix associated to the roots o…
Lattice based integration algorithms: Kronecker sequences and rank-1 lattices
Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki +2
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homo…
Optimal order quadrature error bounds for infinite-dimensional higher order digital sequences
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
Quasi-Monte Carlo (QMC) quadrature rules using higher order digital nets and sequences have been shown to achieve the almost optimal rate of convergence of the worst-case error in…
Construction of interlaced polynomial lattice rules for infinitely differentiable functions
Josef Dick, Takashi Goda, Kosuke Suzuki +1
We study multivariate integration over the -dimensional unit cube in a weighted space of infinitely differentiable functions. It is known from a recent result by Suzuki that the…