During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

In the present paper, we give a survey of the recent results and outline future prospects of
the tensor-structured numerical methods in applications to multidimensional problems in …

Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …

This survey provides an overview of higher-order tensor decompositions, their applications,
and available software. A tensor is a multidimensional or N-way array. Decompositions of …

The paper presents a new scheme for the representation of tensors which is well-suited for
high-order tensors. The construction is based on a hierarchy of tensor product subspaces …

In this paper we introduce a new class of tensor decompositions. Intuitively, we decompose
a given tensor block into blocks of smaller size, where the size is characterized by a set of …

Tensor decomposition is a fundamental unsupervised machine learning method in data
science, with applications including network analysis and sensor data processing. This work …

We present an alternative strategy for truncating the higher-order singular value
decomposition (T-HOSVD). An error expression for an approximate Tucker decomposition …

In the present paper, we discuss the novel concept of super-compressed tensor-structured
data formats in high-dimensional applications. We describe the multifolding or quantics …

Higher order tensor inversion is possible for even order. This is due to the fact that a tensor
group endowed with the contracted product is isomorphic to the general linear group of …