3 citations · 5 across the 4 of their papers we have counts for
6 papers · 1 filter
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…
-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…
Multigrid Monte Carlo Revisited: Theory and Bayesian Inference
Yoshihito Kazashi, Eike H. Müller, Robert Scheichl
Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate norma…
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…
Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces
Takashi Goda, Yoshihito Kazashi, Yuya Suzuki
Randomized quadratures for integrating functions in Sobolev spaces of order , where the integrability condition is with respect to the Gaussian measure, are considered. In…
Sub-optimality of Gauss--Hermite quadrature and optimality of the trapezoidal rule for functions with finite smoothness
Yoshihito Kazashi, Yuya Suzuki, Takashi Goda
The sub-optimality of Gauss--Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order , wh…