Lars Grasedyck

Hierarchical Singular Value Decomposition of Tensors

We define the hierarchical singular value decomposition (SVD) for tensors of order

A projection method to solve linear systems in tensor format

d\geq2

Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs ∗

. This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in

Parallel tensor sampling in the hierarchical Tucker format

d=2

A nearly optimal multigrid method for general unstructured grids

), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical format (

A Review on Adaptive Low-Rank Approximation Techniques in the Hierarchical Tensor Format

\mathcal{H}

Solving an elliptic PDE eigenvalue problem via automated multi-level substructuring and hierarchical matrices

-Tucker) which requires only

Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations

\mathcal{O}((d-1)k^3+dnk)

Influence of finite element discretization on the EEG/MEG forward solution in rabbits

parameters, where

A literature survey of low‐rank tensor approximation techniques

d