4 papers
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…
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…
-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…
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…