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CONTINUITY OF ROOTS, REVISITED

Part of: Real and complex fields Polynomials and matrices Geometric function theory General theory in ordinary differential equations Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  15 August 2018

DARIUSZ BUGAJEWSKI Open the ORCID record for DARIUSZ BUGAJEWSKI [Opens in a new window]  and
PIOTR MAĆKOWIAK Open the ORCID record for PIOTR MAĆKOWIAK [Opens in a new window]
DARIUSZ BUGAJEWSKI
Affiliation:
Optimization and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, ul. Umultowska 87, 61-614 Poznań, Poland email ddbb@amu.edu.pl
PIOTR MAĆKOWIAK*
Affiliation:
Department of Mathematical Economics, Poznań University of Economics and Business, Al. Niepodległości 10, 61-875 Poznań, Poland email piotr.mackowiak@ue.poznan.pl
*
✉piotr.mackowiak@ue.poznan.pl
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Abstract

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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.

Keywords

roots of polynomialscontinuity of roots and solutionslinear differential equations with constant coefficients

MSC classification

Primary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Secondary: 11C08: Polynomials 12D05: Polynomials 34A30: Linear equations and systems, general 65H04: Roots of polynomial equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 448 - 455
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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