Durand–Kerner method: Difference between revisions

Revision as of 04:00, 11 December 2020

Revision as of 06:07, 24 May 2021

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* {{cite conference|last=Weierstraß|first= Karl|author-link=Karl Weierstraß|title=Neuer Beweis des Satzes, dass jede ganze rationale Function einer Veränderlichen dargestellt werden kann als ein Product aus linearen Functionen derselben Veränderlichen|book-title=Sitzungsberichte der königlich preussischen Akademie der Wissenschaften zu Berlin|year=1891|url=http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/anzeige?band=10-sitz/1891-2&seite:int=00000565}}

* {{cite conference|last=Durand|first=E.|book-title=Solutions Numériques des Equations Algébriques |volume=1|editor=Masson |display-editors=etal |title=Equations du type ''F''(''x'') = 0: Racines d'un polynome|year= 1960}}

* {{cite journal|last= Kerner|first= Immo O.|title=Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen|journal=Numerische Mathematik|volume=8|year= 1966|issue= 3|pages= 290–294|doi=10.1007/BF02162564 }}

* {{cite journal|author=Prešić, Marica|title=A convergence theorem for a method for simultaneous determination of all zeros of a polynomial |url=http://elib.mi.sanu.ac.rs/files/journals/publ/48/n042p159.pdf|journal=Publications de l'Institut Mathématique |series=Nouvelle Série|volume=28|pages=158–168 |year=1980 | issue=42}}

* {{cite journal|author=Petkovic, M.S., Carstensen, C. and Trajkovic, M.|title=Weierstrass formula and zero-finding methods|journal=Numerische Mathematik|volume=69|year=1995|issue=3|pages=353–372|doi=10.1007/s002110050097|citeseerx=10.1.1.53.7516}}

* Bo Jacoby, ''Nulpunkter for polynomier'', CAE-nyt (a periodical for Dansk CAE Gruppe [Danish CAE Group]), 1988.

* Agnethe Knudsen, ''Numeriske Metoder'' (lecture notes), Københavns Teknikum.

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* {{cite book|last=Gourdon|first=Xavier|title=Combinatoire, Algorithmique et Geometrie des Polynomes|publisher=École Polytechnique|___location=Paris|year=1996|url=http://algo.inria.fr/gourdon/thesis.html|access-date=2006-08-22|archive-url=https://web.archive.org/web/20061028060132/http://algo.inria.fr/gourdon/thesis.html|archive-date=2006-10-28|url-status=dead}}

* [[Victor Pan]] (May 2002): [https://web.archive.org/web/20060907205721/http://www.cs.gc.cuny.edu/tr/techreport.php?id=26 ''Univariate Polynomial Root-Finding with Lower Computational Precision and Higher Convergence Rates'']. Tech-Report, City University of New York

* {{cite journal|first= Arnold|last= Neumaier|title= Enclosing clusters of zeros of polynomials|journal= Journal of Computational and Applied Mathematics|volume= 156 |year=2003|issue= 2|url=https://www.mat.univie.ac.at/~neum/papers.html#polzer|doi= 10.1016/S0377-0427(03)00380-7|pages= 389389–401|bibcode= 2003JCoAM.156..389N|doi-access= free}}

* Jan Verschelde, ''[http://www2.math.uic.edu/~jan/mcs471f03/Project_Two/proj2/node2.html The method of Weierstrass (also known as the Durand–Kerner method)]'', 2003.

* Bernhard Reinke, Dierk Schleicher, and Michael Stoll, ``[https://arxiv.org/abs/2004.04777 The Weierstrass root finder is not generally convergent]'', 2020