In the past two decades, the density matrix renormalization group (DMRG) has emerged as
an innovative new method in quantum chemistry relying on a theoretical framework very …

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 …

Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

Tensor networks are approximations of high-order tensors which are efficient to work with
and have been very successful for physics and mathematics applications. We demonstrate …

Tensor networks have in recent years emerged as the powerful tools for solving the large-
scale optimization problems. One of the most popular tensor network is tensor train (TT) …

This paper proposes a novel approach to tensor completion, which recovers missing entries
of data represented by tensors. The approach is based on the tensor train (TT) rank, which is …

Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …

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 …

Information about the behavior of dynamical systems can often be obtained by analyzing the
eigenvalues and corresponding eigenfunctions of linear operators associated with a …

The nonlinear autoregressive exogenous (NARX) model shows a strong expression
capacity for nonlinear systems since these systems have limited information about their …