This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. Compared to existing methods based on the functional tensor train format, our approach often reduces the required storage, sometimes considerably, while achieving the same accuracy. In particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96% compared to the algorithm from [Gorodetsky, Karaman and Marzouk, Comput. Methods Appl. Mech. Eng., 347 (2019)] .

翻译：本文提出了扩展函数张量列（EFTT）格式，用于压缩和处理张量积域上的多元函数。我们的压缩算法将张量化切比雪夫插值与完全基于函数评估的低秩近似算法相结合。与现有基于函数张量列格式的方法相比，我们的方法通常能显著减少所需存储空间（有时甚至大幅降低），同时达到相同的精度。特别地，与文献 [Gorodetsky, Karaman and Marzouk, Comput. Methods Appl. Mech. Eng., 347 (2019)] 中的算法相比，我们在实现指定精度所需的函数评估次数上最多减少了超过96%。