Jia-Xin Geng

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20232025

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math.NA2024

Weighted least $ℓ_{p}$ approximation on compact Riemannian manifolds

Jiansong Li, Yun Ling, Jiaxin Geng +1

Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_{2}$ on a compact space, Gröchenig in \cite{G} discussed weighted least squares approximation and least squares quadratur…

math.NA2024

Optimal quadrature errors and sampling numbers for Sobolev spaces with logarithmic perturbation on spheres

Jiaxin Geng, Yun Ling, Jiansong Li +1

In this paper, we study optimal quadrature errors, approximation numbers, and sampling numbers in $L_{2} (S^{d})$ for Sobolev spaces $H^{α, β} (S^{d})$ with logarithmic pert…

math.NA2023

On the power of standard information for tractability for $L_{\infty}$ approximation of periodic functions in the worst case setting

Jiaxin Geng, Heping Wang

We study multivariate approximation of periodic function in the worst case setting with the error measured in the $L_{\infty}$ norm. We consider algorithms that use standard informat…

Weighted least ℓp​ approximation on compact Riemannian manifolds

Optimal quadrature errors and sampling numbers for Sobolev spaces with logarithmic perturbation on spheres

On the power of standard information for tractability for L∞​ approximation of periodic functions in the worst case setting

Weighted least $ℓ_{p}$ approximation on compact Riemannian manifolds

On the power of standard information for tractability for $L_{\infty}$ approximation of periodic functions in the worst case setting