论文标题
扩展功能张量列车格式的近似
Approximation in the extended functional tensor train format
论文作者
论文摘要
这项工作提出了扩展功能张量列（EFTT）格式，用于压缩和使用张量产品域上的多元功能。我们的压缩算法将张力的Chebyshev插值与完全基于函数评估的低级别近似算法结合在一起。与基于功能张量列车格式的现有方法相比，我们方法的适应性通常会导致所需的存储（有时大大减少），同时达到相同的精度。特别是，与来自[Gorodetsky，Karaman和Marzouk，Comput的算法相比，我们将实现规定准确性所需的功能评估次数降低了多达96％以上。方法应用。机械。 Eng。，347（2019）]。
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, the adaptivity of our approach often results in reducing 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)].
