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Mathematics of Computation

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On using symmetric polynomials for constructing root finding methods

Author: Dmitry I. Khomovsky
Journal: Math. Comp. 89 (2020), 2321-2331
MSC (2010): Primary 30C15, 65H05
Published electronically: April 6, 2020
MathSciNet review: 4109568
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Abstract: We propose an approach to constructing iterative methods for finding polynomial roots simultaneously. One feature of this approach is using the fundamental theorem of symmetric polynomials. Within this framework, we reconstruct many of the existing root finding methods. The new results presented in this paper are some modifications of the Durand-Kerner method.

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Additional Information

Dmitry I. Khomovsky
Affiliation: Faculty of Physics, Lomonosov Moscow State University, 1-2 Leninskie Gory, 119991 Moscow, Russia

Keywords: Polynomials, iterative methods, Weierstrass--Durand--Kerner method
Received by editor(s): June 16, 2018
Received by editor(s) in revised form: June 23, 2018, August 2, 2019, and January 13, 2020
Published electronically: April 6, 2020
Article copyright: © Copyright 2020 American Mathematical Society