The hierarchical Tucker format is a storage-efficient scheme to
approximate and represent tensors of possibly high order. From a tensor
network perspective, it represents a network of order-3 tensors without
cycles. Thus, it is a generalization of the Tensor Train or Matrix
Product States (MPS) format.

This talk introduces a Matlab toolbox, along with the underlying
methodology and algorithms, providing a convenient way to work with this
format. The toolbox not only allows for the efficient storage and
manipulation of tensors but also offers a set of tools for the
development of higher-level algorithms.

As an example for the use of the toolbox, an algorithm for solving
high-dimensional linear systems, namely parameter-dependent elliptic
PDEs, is shown. This is joint work with Daniel Kressner, ETH Zurich.