3 citations · 3 across the 10 of their papers we have counts for
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…
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) that…
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…
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…
Quasi-Monte Carlo hyperinterpolation
Congpei An, Mou Cai, Takashi Goda
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2…
A note on unshifted lattice rules for high-dimensional integration in weighted unanchored Sobolev spaces
Takashi Goda
This short article studies a deterministic quasi-Monte Carlo lattice rule in weighted unanchored Sobolev spaces of smoothness . Building on the error analysis by Kazashi and Slo…
-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,…
-approximation using randomized lattice algorithms
Mou Cai, Takashi Goda, Yoshihito Kazashi
We propose a randomized lattice algorithm for approximating multivariate periodic functions over the -dimensional unit cube from the weighted Korobov space with mixed smoothness…
A randomized lattice rule without component-by-component construction
Takashi Goda
We study the multivariate integration problem for periodic functions from the weighted Korobov space in the randomized setting. We introduce a new randomized rank-1 lattice rule wi…
How sharp are error bounds? --lower bounds on quadrature worst-case errors for analytic functions
Takashi Goda, Yoshihito Kazashi, Ken'ichiro Tanaka
Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for…