15 citations · 163 across the 28 of their papers we have counts for
24 papers · 1 filter
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…
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…
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…
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…
An explicit construction of optimal order quasi-Monte Carlo rules for smooth integrands
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
In a recent paper by the authors, it is shown that there exists a quasi-Monte Carlo (QMC) rule which achieves the best possible rate of convergence for numerical integration in a r…
Optimal order quasi-Monte Carlo integration in weighted Sobolev spaces of arbitrary smoothness
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
We investigate quasi-Monte Carlo integration using higher order digital nets in weighted Sobolev spaces of arbitrary fixed smoothness , , defined over the…
Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions
Kosuke Suzuki
We investigate multivariate integration for a space of infinitely times differentiable functions $\mathcal{F}_{s, \boldsymbol{u}} := \{f \in C^\infty [0,1]^s \mid \| f \|_{\mathcal…
Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients
Kosuke Suzuki, Takehito Yoshiki
We establish formulas for the -adic Walsh coefficients of functions in for an integer and give upper bounds on the Walsh coefficients of these functions. We…
The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets
Takashi Goda, Ryuichi Ohori, Kosuke Suzuki +1
In this paper, we study randomized quasi-Monte Carlo (QMC) integration using digitally shifted digital nets. We express the mean square QMC error of the -th discrete approximati…
Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
In this paper we study quasi-Monte Carlo integration of smooth functions using digital nets. We fold digital nets over by means of the -adic tent transformation…
WAFOM on abelian groups for quasi-Monte Carlo point sets
Kosuke Suzuki
In this paper, we study quasi-Monte Carlo (QMC) rules for numerical integration. J. Dick proved a Koksma-Hlawka type inequality for -smooth integrands and gave an explicit const…
The -adic tent transformation for quasi-Monte Carlo integration using digital nets
Takashi Goda, Kosuke Suzuki, Takehito Yoshiki
In this paper we investigate quasi-Monte Carlo (QMC) integration using digital nets over in reproducing kernel Hilbert spaces. The tent transformation, or the baker'…