Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

In this chapter we present numerical methods for low-rank matrix and tensor problems that
explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus …

Sparse tensor decomposition and completion are common in numerous applications,
ranging from machine learning to computational quantum chemistry. Typically, the main …

Tensor learning is a powerful tool for big data analytics and machine learning, eg, gene
analysis and deep learning. However, tensor learning algorithms are compute-intensive …

Tensor methods have gained increasingly attention from various applications, including
machine learning, quantum chemistry, healthcare analytics, social network analysis, data …

This article investigates a fast and highly efficient algorithm to find the strong approximation
inverse of an invertible tensor. The convergence analysis shows that the proposed method …

We introduce the tensor numerical method for solution of the d-dimensional optimal control
problems (d= 2, 3) with spectral fractional Laplacian type operators in constraints discretized …

For fast density functional calculations, a suitable basis that can accurately represent the
orbitals within a reasonable number of dimensions is essential. Here, we propose a new …

In this paper, we propose and analyze the numerical algorithms for fast solution of periodic
elliptic problems in random media in ℝ d R^ d, d= 2, 3 d= 2, 3. Both the two‐dimensional …

This work proposes the extended functional tensor train (EFTT) format for compressing and
working with multivariate functions on tensor product domains. Our compression algorithm …