# Chebyshev polynomials and best rank-one approximation ratio

## TL;DR

This paper explores the extremal properties of Chebyshev polynomials related to tensor approximation, providing new insights into the best rank-one approximation ratio and conditions for tensor minimizers.

## Contribution

It introduces a novel extremal property of Chebyshev polynomials and offers necessary conditions for tensors to minimize the spectral to Frobenius norm ratio.

## Key findings

- Established a new extremal property of Chebyshev polynomials.
- Derived necessary conditions for tensor minimizers.
- Enhanced understanding of tensor approximation ratios.

## Abstract

We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a tensor to be a minimizer of the ratio of spectral and Frobenius norms.