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Title: Acceleration of the Robust Newton Method by the use of the S-iteration
Authors: Gdawiec, Krzysztof
Kotarski, Wiesław
Lisowska, Agnieszka
Keywords: Robust Newton method; S-iteration; Polynomiography
Issue Date: 2021
Citation: "Lecture Notes in Computer Science" Vol. 12742 (2021), s. 330-337
Abstract: In this paper, we propose an improvement of the Robust Newton's Method (RNM). The RNM is a generalisation of the known Newton's root finding method restricted to polynomials. Unfortunately, the RNM is slow. Thus, in this paper, we propose the acceleration of this method by replacing the standard Picard iteration in the RNM by the S-iteration. This leads to an essential acceleration of the modified method. We present the advantages of the proposed algorithm over the RNM using polynomiagraphs and some numerical measures. Moreover, we present its possible application to the generation of artistic patterns.
DOI: 10.1007/978-3-030-77961-0_28
ISBN: 978-3-030-77960-3
Appears in Collections:Artykuły (WNŚiT)

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