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 …

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 …

Tensor completion is a problem of filling the missing or unobserved entries of partially
observed tensors. Due to the multidimensional character of tensors in describing complex …

Work on this book started more than 15 years ago, when I began a revision of a textbook
from 1974 on numerical methods. That book devoted only about 90 pages to matrix …

Operations with tensors, or multiway arrays, have become increasingly prevalent in recent
years. Traditionally, tensors are represented or decomposed as a sum of rank-1 outer …

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 …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF
problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not …

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of
multiway data. The standard alternating least squares algorithm for the CP decomposition …

The lexicon of any natural language encodes a huge number of distinct word meanings. Just
to understand this article, you will need to know what thousands of words mean. The space …