15 citations · 110 across the 16 of their papers we have counts for
17 papers
Digital Nets on Cubature Nodes: Inheriting Cubature Accuracy on Low-Dimensional Projections
Takehito Yoshiki
Base-2 digital nets are practical high-dimensional integration rules: the sample budget can be chosen independently of the ambient dimension, and the generating matrices pr…
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,\…
Richardson extrapolation of polynomial lattice rules
Josef Dick, Takashi Goda, Takehito Yoshiki
We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness defined over the -dimensional unit cube. We…
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…
Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions
Matsumoto Makoto, Ryuichi Ohori, Takehito Yoshiki
In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in by a digital net over . We show that the r…
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…
Bounds on Walsh coefficients by dyadic difference and a new Koksma-Hlawka type inequality for Quasi-Monte Carlo integration
Takehito Yoshiki
In this paper we give a new Koksma-Hlawka type inequality for Quasi-Monte Carlo (QMC) integration. QMC integration of a function by a finite…
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…
A Lower Bound on WAFOM
Takehito Yoshiki
We give a lower bound on Walsh figure of merit (WAFOM), which is a parameter to estimate the integration error for quasi-Monte Carlo (QMC) integration by a point set called a digit…
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…