Iteration methods for finding all zeros of a polynomial simultaneously
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- by Oliver Aberth PDF
- Math. Comp. 27 (1973), 339-344 Request permission
Abstract:
Durand and Kerner independently have proposed a quadratically convergent iteration method for finding all zeros of a polynomial simultaneously. Here, a new derivation of their iteration equation is given, and a second, cubically convergent iteration method is proposed. A relatively simple procedure for choosing the initial approximations is described, which is applicable to either method.References
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E. Durand, Solutions Numériques des Équations Algébriques. Tome I: Equations du Type $F(x) = 0$; Racines d’un Polynôme, Masson, Paris, 1960. MR 22 #12714.
- Immo O. Kerner, Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen, Numer. Math. 8 (1966), 290–294 (German). MR 203931, DOI 10.1007/BF02162564
- Morris Marden, Geometry of polynomials, 2nd ed., Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
- Brian T. Smith, Error bounds for zeros of a polynomial based upon Gerschgorin’s theorems, J. Assoc. Comput. Mach. 17 (1970), 661–674. MR 279998, DOI 10.1145/321607.321615
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 339-344
- MSC: Primary 65H05
- DOI: https://doi.org/10.1090/S0025-5718-1973-0329236-7
- MathSciNet review: 0329236