97 citations · 225 across the 33 of their papers we have counts for
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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…
Breaking quadrature exactness: A spectral method for the Allen--Cahn equation on spheres
Hao-Ning Wu, Xiaoming Yuan
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions w…
The springback penalty for robust signal recovery
Congpei An, Hao-Ning Wu, Xiaoming Yuan
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback p…
An ADMM-Newton-CNN Numerical Approach to a TV Model for Identifying Discontinuous Diffusion Coefficients in Elliptic Equations: Convex Case with Gradient Observations
Wenyi Tian, Xiaoming Yuan, Hangrui Yue
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse pr…
Adaptive Primal-Dual Hybrid Gradient Methods for Saddle-Point Problems
Tom Goldstein, Min Li, Xiaoming Yuan +2
The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to…