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 dimension weights.

中文翻译：

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连续函数的张量近似方案分析

在本文中，我们分析了连续函数的张量近似方案。我们假设要逼近的函数位于各向同性 Sobolev 空间中，并讨论在 Tucker 张量格式或张量序列格式的连续模拟中逼近此函数时的成本。我们特别表明，当所考虑的 Sobolev 空间提供适当的维度权重时，两种近似的成本都是维度稳健的。