11 papers
Multivariate integration and approximation in weighted Sobolev spaces of low fractional smoothness
Mou Cai, Takashi Goda
The weighted half-period cosine space has often been employed in the theory of quasi-Monte Carlo methods for multivariate integration and approximation of non-periodic functions. F…
Optimality of quasi-Monte Carlo methods and suboptimality of the sparse-grid Gauss--Hermite rule in Gaussian Sobolev spaces
Yoshihito Kazashi, Yuya Suzuki, Takashi Goda
Optimality of several quasi-Monte Carlo methods and suboptimality of the sparse-grid quadrature based on the univariate Gauss--Hermite rule is proved in the Sobolev spaces of mixed…
A note on approximation in weighted Korobov spaces via multiple rank-1 lattices
Mou Cai, Takashi Goda
This paper studies the multivariate approximation of functions in weighted Korobov spaces using multiple rank-1 lattice rules. It has been shown by Kämmerer and Volkmer (2019) tha…
A lattice algorithm with multiple shifts for function approximation in Korobov spaces
Mou Cai, Josef Dick, Takashi Goda
In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in la…
Universal -approximation using median lattice algorithms
Zexin Pan, Takashi Goda, Peter Kritzer
We study the problem of multivariate -approximation of functions in a weighted Korobov space using a median lattice-based algorithm recently proposed by the authors. In the or…
-approximation using median lattice algorithms
Zexin Pan, Peter Kritzer, Takashi Goda
In this paper, we study the problem of multivariate -approximation of functions belonging to a weighted Korobov space. We propose and analyze a median lattice-based algorithm,…