On the determination of the safe initial approximation for the Durand-Kerner algorithm

In this paper, applying the majorant function method, we present a new proof of the convergence of the Durand-Kerner method, and obtain a greater computable radius estimation of safe initial discs. This result is an improvement of all results now available. Furthermore, combining the Kuhn algorithm...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 38; no. 1; pp. 447 - 456
Main Authors Deren, Wang, Fengguang, Zhao
Format Journal Article
LanguageEnglish
Published Elsevier B.V 23.12.1991
Subjects
circular iteration
complex polynomial
Durand-Kerner algorithm
Kuhn algorithm
majorant functions
safe initial approximation
safe initial approximation
complex polynomial
Durand-Kerner algorithm
Kuhn algorithm
majorant functions
circular iteration
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ISSN0377-0427
1879-1778
DOI10.1016/0377-0427(91)90188-P

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Summary:In this paper, applying the majorant function method, we present a new proof of the convergence of the Durand-Kerner method, and obtain a greater computable radius estimation of safe initial discs. This result is an improvement of all results now available. Furthermore, combining the Kuhn algorithm for solving all zeros of polynomials, we obtain a discriminant to get safe initial discs. Finally, we compare the complexity between the Durand-Kerner algorithm and several known results, and the numerical results show the superiority of our result.
ISSN:0377-0427
1879-1778
DOI:10.1016/0377-0427(91)90188-P