Tensor solvers for high-dimensional eigenvalue problems (Maxim Rakhuba - ETH Zurich)

14.05.2019 14:00 – 15:00

This talk focuses on the solution of high-dimensional eigenvalue problems, which naturally arise, for example, in Schroedinger-type equations. It has been verified that in a variety of cases eigenvectors can be well approximated using tensor decompositions. Nevertheless, finding them can be a challenging task if, say, the number of eigenvectors to be computed is large, or discretization is performed on very fine meshes. We address these issues by developing new iterative methods that are capable of efficiently calculating from several to hundreds of eigenstates in high dimensions. The proposed methods are based on Riemannian optimization techniques and some classical iterative methods such as Jacobi-Davidson, LOBPCG, and ADI. To make the methods efficient and easy to implement, we additionally utilize automatic differentiation techniques. We showcase our methods by solving vibrational Schroedinger equation and equations arising in density functional theory.

Lieu

Room 623, Séminaire d'analyse numérique

entrée libre