Continuity of roots, revisited

Dariusz Bugajewski , Piotr Maćkowiak

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.
Author Dariusz Bugajewski - Adam Mickiewicz University (UAM)
Dariusz Bugajewski,,
-
, Piotr Maćkowiak (WIiGE / KEM)
Piotr Maćkowiak,,
- Department of Mathematical Economics
Journal seriesBulletin of the Australian Mathematical Society, ISSN 0004-9727, (A 20 pkt)
Issue year2018
Vol98
No3
Pages448-455
Publication size in sheets0.5
Keywords in Englishroots of polynomials, continuity of roots and solutions, linear differential equations with constant coefficients
ASJC Classification2600 General Mathematics
DOIDOI:10.1017/S0004972718000709
URL https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/continuity-of-roots-revisited/13908DB719483408448DCF29B26EF1E4#fndtn-information
Languageen angielski
Score (nominal)20
Score sourcejournalList
ScoreMinisterial score = 20.0, 12-03-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.908; WoS Impact Factor: 2018 = 0.592 (2) - 2018=0.664 (5)
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UwagiFirst Online 15 Aug 2018
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