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Title: Visual Analysis of the Newton's Method with Fractional Order Derivatives
Authors: Gdawiec, Krzysztof
Kotarski, Wiesław
Lisowska, Agnieszka
Keywords: fractional derivative; Newton method; root-finding; polynomiography
Issue Date: 2019
Citation: Symmetry, iss. 11(9) (2019), art. no 1143, s. 1-27
Abstract: The aim of this paper is to investigate experimentally and to present visually the dynamics of the processes in which in the standard Newton's root finding method the classic derivative is replaced by the fractional Riemann-Liouville or Caputo derivatives. These processes applied to polynomials on the complex plane produce images showing basins of attractions for polynomial zeros or images representing the number of iterations required to obtain polynomial roots. These latter images were called by Kalantari as polynomiographs. We use both: the colouring by roots to present basins of attractions, and the colouring by iterations that reveal the speed of convergence and dynamic properties of processes visualised by polynomiographs.
DOI: 10.3390/sym11091143
ISSN: 2073-8994
Appears in Collections:Artykuły (WNŚiT)

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