12 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…