The Tensor Train Extension

In 10 dimensions, an analog of a matrix is a tensor. In the tensor method, you don't want to be sampling. What we have come up with is a functional tensor train extension of the tensor train that we use the same basis functions as in generalized stochastic sampling. But what is very important here is that the coefficients corresponding to these basis functions are represented in the lower end decomposition. So we can actually combine them. And so this tensor train is a bit orthogonal to the no stochastic one. However, they serve the same goal, how to set up basis functions with the coefficients such that the number is limited but still covers multi