### Conveners

#### Day I: Session I

- Peter Benner ()

#### Day I: Session II

- Boris Khoromskij (Max-Planck Institute for Mathematics in the Sciences, Leipzig)

Sparse tensor decompositions have become increasingly popular in the literature due to their capability to naturally model high dimensional sparse data with many features, and glean hidden relations owing to underlying low-rank structures within the data. They have been successfully employed in many application settings including recommender systems, graph analytics, healthcare data analytics,...

We propose guaranteed and fully computable upper bound on the energy norm of the error in low rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from Euler-Lagrange equations for a complementary flux reconstruction problem, which are solved in the low rank TT representation using the block Alternating Linear...

We consider the rank-structured tensor approach for numerical modeling of long-range potentials in many-particle systems. The method of grid-based assembled tensor summation of the electrostatic potentials on 3D finite lattices [3] exhibits the computational complexity of the order of $O(L)$ which is much less than $O(L^3)$ in traditional Ewald-type summation.

Novel range-separated (RS)...

We prove the convergence of the multigrid method for parameter-dependent symmetric positive definite linear systems. We present the smoothing and approximation properties for such problems and prove the smoothing property for the parameter-dependent damped Richardson as well as the parameter-dependent damped Jacobi method.

Our theoretical results require a parameter-dependent representation...

We discuss the problem of computing roots of systems of multivariate polynomials by approaches from numerical linear and multilinear algebra.The key concept in our approach is the Macaulay matrix, a large and highly structured matrix that contains the coefficients of the polynomials systems. The roots can be retrieved from the nullspace of this matrix. We then show how this root retrieval can...

Automatic Face Recognition has become increasingly important in the past few years due to its several applications in daily life. Numerical linear algebra tools have been extensively used for classification purposes. However, since several factors can affect the image, multilinear algebra tools seem to be a natural choice to deal with image classification.

We propose a new algorithm based...