4 papers
From Pólya's Conditions to a Complete Characterization of the Convergence of Hyperinterpolation
Congpei An, Xiannan Hu, Xiaoming Yuan
It has remained open to identify the necessary and sufficient conditions for the convergence of hyperinterpolation since it was introduced by Sloan in 1995. We show that the…
An Optimization Approach to Weight Collocation for Scattered Spherical Data
Congpei An, Xiannan Hu, Xiaoming Yuan
We introduce an optimization approach for constructing spherical quadrature rules on arbitrarily scattered data. Rather than designing node placements, the new approach focuses on…
Regularized Barzilai-Borwein method
Congpei An, Xin Xu
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize…
Hard thresholding hyperinterpolation over general regions
Congpei An, Jiashu Ran
This paper proposes a novel variant of hyperinterpolation, called hard thresholding hyperinterpolation. This approximation scheme of degree leverages a hard thresholding operat…