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：这项工作提出了用于压缩和与多变功能一起在高产品域进行压缩和工作的扩展功能高压列车(EFTT)格式。我们的压缩算法将高压切比谢夫内插和完全基于功能评价的低级近似算法结合起来。与基于功能高压列车格式的现有方法相比,我们的方法往往会减少所需的存储量,有时会大大降低,同时达到同样的准确性。特别是,我们把实现规定的准确性所需的功能评价数量比[Gorodetsky、Karaman和Marzouk,Comput.方法Appl. Mech. Eng., 347 (2019年)]的算法减少96%以上。