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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| Published in | Journal of computational and applied mathematics Vol. 38; no. 1; pp. 447 - 456 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
23.12.1991
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/0377-0427(91)90188-P |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Deren, Wang Fengguang, Zhao |
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| Cites_doi | 10.1016/0771-050X(82)90007-9 10.1007/BF02241861 10.1007/BF02162564 |
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| Copyright | 1991 |
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| Keywords | safe initial approximation complex polynomial Durand-Kerner algorithm Kuhn algorithm majorant functions circular iteration |
| Language | English |
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| References | Kerner (BIB3) 1966; 8 Petković, Stefanovic (BIB5) 1985; 3 Durand (BIB1) 1960 Petković (BIB4) 1982; 8 Wang, Zhao (BIB6) 1989; 43 Wang, Zheng (BIB7) 1984; 2 Karamardian (BIB2) 1977 Kerner (10.1016/0377-0427(91)90188-P_BIB3) 1966; 8 Petković (10.1016/0377-0427(91)90188-P_BIB5) 1985; 3 Wang (10.1016/0377-0427(91)90188-P_BIB6) 1989; 43 Durand (10.1016/0377-0427(91)90188-P_BIB1) 1960 Petković (10.1016/0377-0427(91)90188-P_BIB4) 1982; 8 Wang (10.1016/0377-0427(91)90188-P_BIB7) 1984; 2 Karamardian (10.1016/0377-0427(91)90188-P_BIB2) 1977 |
| References_xml | – year: 1977 ident: BIB2 article-title: Fixed Points-Algorithm and Applications – volume: 2 start-page: 305 year: 1984 end-page: 309 ident: BIB7 article-title: The quasi-Newton in paralled circular iteration publication-title: J. Comput. Math. – year: 1960 ident: BIB1 publication-title: Solutions Numériques des Equations Algébriques, Tome 1: Equation du Type F(χ)=0, Racines d'un Polynome – volume: 43 start-page: 187 year: 1989 end-page: 197 ident: BIB6 article-title: Complexity analysis of a process for simultaneously obtaining all zeros of polynomials publication-title: Computing – volume: 8 start-page: 290 year: 1966 end-page: 294 ident: BIB3 article-title: Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen publication-title: Numer. Math. – volume: 8 start-page: 51 year: 1982 end-page: 56 ident: BIB4 article-title: On an iterative method for simultaneous inclusion of polynomial complex zeros publication-title: J. Comput. Appl. Math. – volume: 3 start-page: 63 year: 1985 end-page: 95 ident: BIB5 article-title: On the simultaneous method of the second order for finding polynomial complex zeros in circular arithmetic publication-title: Fib. – volume: 8 start-page: 51 issue: 1 year: 1982 ident: 10.1016/0377-0427(91)90188-P_BIB4 article-title: On an iterative method for simultaneous inclusion of polynomial complex zeros publication-title: J. Comput. Appl. Math. doi: 10.1016/0771-050X(82)90007-9 – volume: 3 start-page: 63 year: 1985 ident: 10.1016/0377-0427(91)90188-P_BIB5 article-title: On the simultaneous method of the second order for finding polynomial complex zeros in circular arithmetic publication-title: Fib. – volume: 43 start-page: 187 year: 1989 ident: 10.1016/0377-0427(91)90188-P_BIB6 article-title: Complexity analysis of a process for simultaneously obtaining all zeros of polynomials publication-title: Computing doi: 10.1007/BF02241861 – year: 1977 ident: 10.1016/0377-0427(91)90188-P_BIB2 – year: 1960 ident: 10.1016/0377-0427(91)90188-P_BIB1 publication-title: Solutions Numériques des Equations Algébriques, Tome 1: Equation du Type F(χ)=0, Racines d'un Polynome – volume: 8 start-page: 290 year: 1966 ident: 10.1016/0377-0427(91)90188-P_BIB3 article-title: Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen publication-title: Numer. Math. doi: 10.1007/BF02162564 – volume: 2 start-page: 305 year: 1984 ident: 10.1016/0377-0427(91)90188-P_BIB7 article-title: The quasi-Newton in paralled circular iteration publication-title: J. Comput. Math. |
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| StartPage | 447 |
| SubjectTerms | circular iteration complex polynomial Durand-Kerner algorithm Kuhn algorithm majorant functions safe initial approximation |
| Title | On the determination of the safe initial approximation for the Durand-Kerner algorithm |
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