Beyond Descartes’ rule of signs-Reference-Cited by-同舟云学术

Beyond Descartes’ rule of signs

Published:2023-06-15 Issue:2 Volume:6 Page:128-141
ISSN:2651-2939
Container-title:Constructive Mathematical Analysis
language:
Short-container-title:

Author:

KOSTOV Vladimir¹^ORCID

Affiliation:

1. Universit'e C^ote d'Azur, CNRS, LJAD

Abstract

We consider real univariate polynomials with all roots real. Such a polynomial with c sign changes and p sign preservations in the sequence of its coefficients has c positive and p negative roots counted with multiplicity. Suppose that all moduli of roots are distinct; we consider them as ordered on the positive half-axis. We ask the question: If the positions of the sign changes are known, what can the positions of the moduli of negative roots be? We prove several new results which show how far from trivial the answer to this question is.

Publisher

Constructive Mathematical Analysis

Subject

Applied Mathematics,Numerical Analysis,Analysis

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