Heping Wang

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20162022

most citedApproximation and quadrature by weighted least squares polynomials on the sphere

2 citations · 7 across the 8 of their papers we have counts for

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7 papers · 1 filter

math.NA2022

Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball

Jiansong Li, Heping Wang

We consider the numerical integration $INT_{d} (f) = \int_{B^{d}} f (x) w_{μ} (x) d x$ for the weighted Sobolev classes $B W_{p, μ}^{r}$ and the weighted Besov classes $BB_τ^r(L…

math.NA2022

Weighted $ℓ_{q}$ approximation problems on the ball and on the sphere

Jiansong Li, Heping Wang

Let $L_{q, μ}, 1 \leq q < \infty, μ \geq 0,$ denote the weighted $L_{q}$ space with the classical Jacobi weight $w_{μ}$ on the ball $B^{d}$ . We consider the weighted least $ℓ_{q}$ appr…

math.NA2021

On the power of standard information for tractability for $L_{2}$ -approximation in the average case setting

Wanting Lu, Heping Wang

We study multivariate approximation in the average case setting with the error measured in the weighted $L_{2}$ norm. We consider algorithms that use standard information $Λ^{\rm std…

math.NA2021★ 2 cited

On the power of standard information for tractability for $L_{2}$ -approximation in the randomized setting

Wanting Lu, Heping Wang

We study approximation of multivariate functions from a separable Hilbert space in the randomized setting with the error measured in the weighted $L_{2}$ norm. We consider algorithms…

math.NA2021★ 2 cited

Approximation and quadrature by weighted least squares polynomials on the sphere

Wanting Lu, Heping Wang

Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_{2}$ on a usual compact space $M$ , Gröchenig introduced the weighted least squares polynomials and the least squ…

math.NA2019★ 2 cited

Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings

JiDong Hao, Heping Wang

In this paper, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences $a = {a_{j}}_{j \geq 1}$ and ${\bf b}=\{b_j\}_{j…

Optimal randomized quadrature for weighted Sobolev and Besov classes with the Jacobi weight on the ball

Weighted ℓq​ approximation problems on the ball and on the sphere

On the power of standard information for tractability for L2​-approximation in the average case setting

On the power of standard information for tractability for L2​-approximation in the randomized setting

Approximation and quadrature by weighted least squares polynomials on the sphere

Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings

Weighted $ℓ_{q}$ approximation problems on the ball and on the sphere

On the power of standard information for tractability for $L_{2}$ -approximation in the average case setting

On the power of standard information for tractability for $L_{2}$ -approximation in the randomized setting