This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.

翻译：本文介绍了一种建立明确的抗拉力(TT)表达方式的方法。我们显示,一大批的抗拉力可以以稀疏的TT核心来明确代表,在许多情况下可以获得最佳的TT级。 数字实验表明,我们的方法在一些实际应用中超过了现有的方法,包括游戏理论问题。 对操作次数的理论估计表明,在诸如长期计算等一些问题中,我们的方法接近于已知的最佳模拟方法,而这种方法是用完全不同的方法获得的。