摘要
文章介绍了数据科学与计算数学交叉学科中概率宽度问题的研究现状,阐明了计算复杂性与宽度理论之间的联系,给出了不同框架下Gel̓fand宽度的定义,并研究了信息函数类在不同计算模型下的逼近特性。基于离散化思想,文章精确刻画了赋予Gussian测度的多元Sobolev空间MWr 2在Sq尺度下的概率Gel̓fand宽度的阶数。
This article introduces the research status of probability width problem in the interdisciplinary field of data science and computational mathematics,clarifies the relationship between computational complexity and width theory,provides the definition of Gel̓fand width under different frameworks,and studies the approximation characteristics of information function classes under different computational models.Based on the idea of discretization,the article accurately r characterizes the order of the probability Gel̓fand width of the multivariate Sobolev spaceMW2 given the Gussian measure at the Sq scale.
作者
吴瑞欢
李冱岸
李峰旭
WU Ruihuan;LI Hu̓an;LI Fengxu(North China University of Technology,Beijing 100144,China)
