PIMS-CRG Seminar / UCM Scientific Computing and Data Science Seminar: Yingda Cheng

In this talk, we present two algorithms associated with Tucker tensor format. The first is to obtain the Tucker tensor based on a new cross approximation we developed, called Cross^2-DEIM. This method samples a few fibers (proportionate to the multi-linear rank) in each mode in a FSTD2 fashion. We use DEIM index selection for both the main and complement index sets. It is shown to be more efficient in computing the Tucker tensor format than existing cross approximations. The second method is a solver for nonlinear tensor equations in Tucker format by Anderson Acceleration (AA). This is an extension of our prior results of low rank AA. We show the the method works well for benchmark problems, such as Bratu problem and Allen-Cahn equations. This is joint work with Daniel Appelo (VT).