Abstract
Conditions for the convergence of iteration methods for the simultaneous approximation of polynomial complex roots, treated in the literature, are most frequently based on unattainable data. In this paper we give simple initial conditions involving only initial approximations to the roots of a polynomial and the polynomial degree. Convergence theorems are stated for the simultaneous methods in ordinary complex arithmetic and complex interval arithmetic.
Zusammenfassung
Die in der Literatur behandelten hinreichenden Bedingungen an die Anfangsdaten für die Konvergenz von iterativen Verfahren zur simultanen Berechnung von komplexen Polynomnullstellen basieren häufig auf nicht erhältlichen Daten. In dieser Arbeit geben wir einfache hinreichende Bedingungen an, die nur die Anfangsnäherungen für die Nullstellen und den Grad des Polynomes betreffen. Für die Simultanverfahren in komplexer Arithmetick and komplexer Intervallarithmetik werden Konvergenzsätze formuliert.
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Petković, M.S. On initial conditions for the convergence of simultaneous root finding methods. Computing 57, 163–177 (1996). https://doi.org/10.1007/BF02276878
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DOI: https://doi.org/10.1007/BF02276878