Abstract
The modified Newton method for multiple roots is organized in an interval method to include simultaneously the distinct roots of a given polynomialP in complex circular interval arithmetic. A condition on the starting disks which ensures convergence is given, and convergence is shown to be quadratic. As a consequence, a simple parallel algorithm to approach all the distinct roots ofP is derived from the modified Newton method.
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Communicatef by F. Zirilli
The research reported in this paper has been made possible through the support and the sponsorship of the Italian Government through the Ministero per l'Universitá e la Ricerca Scientifica under Contract MURST 60%, 1990 at the Universitá di L'Aquila.
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Recchioni, M.C. Modified Newton method in circular interval arithmetic. J Optim Theory Appl 86, 223–244 (1995). https://doi.org/10.1007/BF02193468
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DOI: https://doi.org/10.1007/BF02193468