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 …

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

Machine learning and data mining algorithms are becoming increasingly important in
analyzing large volume, multi-relational and multi--modal datasets, which are often …

We resume the recent successes of the grid-based tensor numerical methods and discuss
their prospects in real-space electronic structure calculations. These methods, based on the …

Many numerical approximations rely on a simple iteration, X j+ 1= f (X j), to generate a
sequence {Xj} of approximations to a certain target. A doubling algorithm is an idea to …

We present a method to construct an efficient approximation to the bare exchange and
screened direct interaction kernels of the Bethe–Salpeter Hamiltonian for periodic solid state …

Large scale multidimensional data are often available as multiway arrays or higher-order
tensors which can be approximately represented in distributed forms via low-rank tensor …

In this paper, we propose and study two approaches to approximate the solution of the
Bethe–Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both …

We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format
which aims for numerical modeling of the 3D long-range interaction potentials in …

The eigenproblem for complex J-symmetric matrices HC=[ACD− AT], A, C= CT, D= DT∈ C
n× n is considered. A proof of the existence of a transformation to the complex J-symmetric …