A literature survey of low-rank tensor approximation techniques

TL;DR

This survey reviews recent developments in low-rank tensor approximation techniques, highlighting their importance in scientific computing for solving large-scale linear and multilinear algebra problems, especially for function-related tensors.

Contribution

It provides a comprehensive overview of current research in low-rank tensor approximation, emphasizing recent advances and applications in scientific computing.

Findings

Low-rank tensor approximation effectively addresses large-scale algebra problems.

Recent methods improve efficiency for function-related tensors.

The survey identifies key challenges and future directions in the field.

Abstract

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 would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors.