CONTINUITY OF ROOTS, REVISITED

Author:

BUGAJEWSKI DARIUSZORCID,MAĆKOWIAK PIOTRORCID

Abstract

The aim of this note is to give a simple topological proof of the well-known result concerning continuity of roots of polynomials. We also consider a more general case with polynomials of a higher degree approaching a given polynomial. We then examine the continuous dependence of solutions of linear differential equations with constant coefficients.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference6 articles.

1. Matrix Analysis

2. An Alternate Proof of the Continuity of the Roots of a Polynomial

3. Roots and polynomials as Homeomorphic spaces

4. Large roots yield large coefficients: an addendum to “The roots of a polynomial vary continuously as a function of the coefficients”;Harris;Proc. Amer. Math. Soc.,1988

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