# A sequence of polynomials with optimal condition number

## TL;DR

This paper presents an explicit sequence of univariate polynomials of any degree that achieve the optimal condition number, addressing a long-standing problem in numerical analysis.

## Contribution

It provides a constructive solution to the problem of finding polynomials with optimal condition number, solving a question posed in 1993.

## Key findings

- Explicit sequence of polynomials with optimal condition number
- Addresses a problem posed by Shub and Smale in 1993
- Advances understanding of polynomial condition numbers

## Abstract

We find an explicit sequence of univariate polynomials of arbitrary degree with optimal condition number. This solves a problem posed by Michael Shub and Stephen Smale in 1993.