Randomized algorithms for rounding in the Tensor-Train format

Understand

The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors.

• TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equations.
• For many of these problems, computing the solution explicitly would require an infeasible amount of memory and computational time.
• While the TT format makes these problems tractable, iterative techniques for solving the PDEs must be adapted to perform arithmetic while maintaining the implicit structure.