Durand–Kerner method: Difference between revisions

Revision as of 18:46, 6 September 2020

Revision as of 18:46, 6 September 2020

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== Example ==

This example is from the reference 1992. The equation solved is {{nowrap|1=''x''³ − 3''x''² + 3''x'' − 5 = 0}}. The first 4 iterations move ''p'', ''q'', ''r'' seemingly chaotically, but then the roots are located to 1 decimal. After iteration number 5 we have 4 correct decimals, and the subsequent iteration number 6 confirms that the computed roots are fixed. This general behaviour is characteristic for the method. Also notice that, in this example, the roots are used as soon as they are computed in each iteration. In other words, the computation of each second column uses the value of the previous computed columns.

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

* Bo Jacoby, ''Numerisk løsning af ligninger'', Bygningsstatiske meddelelser (Published by Danish Society for Structural Science and Engineering) volume 63 no. 3-4, 1992, pp. 83–105.

* {{cite book|last=Gourdon|first=Xavier|title=Combinatoire, Algorithmique et Geometrie des Polynomes|publisher=EcoleÉcole 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|url=https://www.mat.univie.ac.at/~neum/papers.html#polzer|doi= 10.1016/S0377-0427(03)00380-7|pages= 389|doi-access= free}}