Publications by Michael Maximilian Steinlechner

Riemannian Optimization For High-Dimensional Tensor Completion

Tensor completion aims to reconstruct a high-dimensional data set where the vast majority of entries is missing. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem rest ...

Siam Publications2016

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Michael Maximilian Steinlechner

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

EPFL2016

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

Daniel Kressner, André Uschmajew, Michael Maximilian Steinlechner

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...

Siam Publications2014

Low-rank tensor completion by Riemannian optimization

Daniel Kressner, Michael Maximilian Steinlechner

In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques on the manifold of tensors of fixed multilinear rank. More spe ...

Springer2014