随机弱容许网格
Randomized weakly admissible meshes
摘要：
连续实值域上的弱容许网格（WAM）是一系列离散网格，使得网格上多项式的离散最大范数与域上多项式的上确界范数相当。网格大小和可比常数的渐近增长率必须以受控的方式增长。在本文中，我们将WAM的概念推广到不一定是多项式函数的层次子空间，并分析了随机采样的特定策略作为一种技术，用于生成WAM的。我们的主要结果表明，WAM的和他们的更强的变体，容许网格（AM），可以通过随机抽样产生，我们的分析提供了具体的估计增长的网格和离散连续可比常数。
英文摘要：
A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic rate of growth of the grid sizes and of the comparability constants must grow in a controlled manner. In this paper, we generalize the notion of a WAM to a hierarchical subspaces of not necessarily polynomial functions, and we analyze particular strategies for random sampling as a technique for generating WAM's. Our main results show that WAM's and their stronger variant, admissible meshes (AM's), can be generated by random sampling, and our analysis provides concrete estimates for growth of both the meshes and the discrete-continuum comparability constants.
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