A sequence of polynomials with optimal condition number-Reference-Cited by-同舟云学术

A sequence of polynomials with optimal condition number

Published:2020-12-08 Issue:1 Volume:34 Page:219-244
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Beltrán Carlos,Etayo Ujué,Marzo Jordi,Ortega-Cerdà Joaquim

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.

Funder

Austrian Science Fund

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/jams/2021-34-01/S0894-0347-2020-00956-0/jams956_AM.pdf

Reference22 articles.

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2. The diamond ensemble: a constructive set of spherical points with small logarithmic energy;Beltrán, Carlos;J. Complexity,2020

3. Fast linear homotopy to find approximate zeros of polynomial systems;Beltrán, Carlos;Found. Comput. Math.,2011

4. Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere;Bétermin, Laurent;Constr. Approx.,2018

5. Complexity and Real Computation

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