In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in the continuous analogue of the Tucker tensor format or of the tensor train format. We especially show that the cost of both approximations are dimension-robust when the Sobolev space under consideration provides appropriate weights.
翻译:在本篇文章中,我们分析了连续功能的“虫近似”计划。我们假设,所要估计的功能在于一个异热带的索博列夫空间,并讨论以连续的塔克高尔格式或高拉列车格式等同该功能时的成本。我们特别表明,当所考虑的索博列夫空间提供适当的重量时,两种近似的成本都是维-紫外线。