AIC Seminar: Andre Uschmajew

Accept our invitation to the AIC seminar on September 2, 2022 at 11 a.m. in the seminar room KN:E-205. Researcher Andre Uschmajew from the Max Planck Institute for Mathematics in Science will give a talk Tensor product approximation of linear operators on matrix spaces.

Lecturer

Andre Uschmajew is Max Planck Research Group Leader for the group Tensors and Optimization at MPI MiS in Leipzig. His research is on low-rank approximation of matrices and tensors, multivariate functions, and high-dimensional equations. He is particularly interested in the algebraic and geometric structures that underlie multilinear representations of low-rank matrix and tensor manifolds, and their implications on the applicability and convergence of numerical optimization methods.

Abstract

Tensor product approximation of linear operators on matrix spaces

Tensor structured linear operators play an important role in matrix equations and low-rank modeling. Motivated by this we consider the problem of approximating a matrix by a sum of Kronecker products. It is known that an optimal approximation in Frobenius norm can be obtained from the singular value decomposition of a rearranged matrix, but when the goal is to approximate the matrix as a linear map, an operator norm would be a more appropriate error measure. We present an alternating optimization approach for the corresponding approximation problem in spectral norm that is based on semidefinite programming, and report on its practical performance for small examples. This is joint work with Venkat Chandrasekaran and Mareike Dressler.