论文标题
一线力解放了
Needlets Liberated
论文作者
论文摘要
Narcowich，Petrushev和Ward引入了球形的一面，为球体上的功能提供了多项式近似的多分辨率序列。一边的构造利用到给定程度的多项式准确的集成规则。本文的目的是通过用Brauchart，Saff，Sloan和Womersley介绍的QMC设计代替QMC设计来放松整合规则的精确性。这样的集成规则（在此允许非平等的立即权重在此处概括）提供了相同的渐近顺序，类似于Sobolev Spaces $ \ Mathbb {H}^s $的确切规则，但更易于获得数值。通过这样的规则，我们构建了``广义的一号''。本文提供了一个错误分析，该分析允许将原始的头号替换为通用的头号，更普遍地分析了一种混合方案，其中较低级别的一名阵线是传统类型的，而新的广义二角则用于一定数量的较高级别。数值实验完成了论文。
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet construction makes use of integration rules that are exact for polynomials up to a given degree. The aim of the present paper is to relax the exactness of the integration rules by replacing them with QMC designs as introduced by Brauchart, Saff, Sloan, and Womersley (2014). Such integration rules (generalised here by allowing non-equal cubature weights) provide the same asymptotic order of convergence as exact rules for Sobolev spaces $\mathbb{H}^s$, but are easier to obtain numerically. With such rules we construct ``generalised needlets''. The paper provides an error analysis that allows the replacement of the original needlets by generalised needlets, and more generally, analyses a hybrid scheme in which the needlets for the lower levels are of the traditional kind, whereas the new generalised needlets are used for some number of higher levels. Numerical experiments complete the paper.
