7 papers
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 for…
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…
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…
-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…
Parameter choice strategies for regularized least squares approximation of noisy continuous functions on the unit circle
Congpei An, Mou Cai
This paper explores the incorporation of Tikhonov regularization into the least squares approximation scheme using trigonometric polynomials on the unit circle. This approach encom…
Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points
Congpei An, Mou Cai
In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on named Lasso trigonometric interpolation. This approximation is an $…