7 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) tha…
Worst-case -approximation of periodic functions using median lattice algorithms
Zexin Pan, Mou Cai, Josef Dick +2
We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space with smoothness in the Lebesgue norm …
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…
-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…
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…