http://hdl.handle.net/20.500.12128/20401
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. |
URI: | http://hdl.handle.net/20.500.12128/20401 |
DOI: | 10.1007/978-3-030-77961-0_28 |
ISBN: | 978-3-030-77960-3 978-3-030-77961-0 |
Appears in Collections: | Artykuły (WNŚiT) |
File | Description | Size | Format | |
---|---|---|---|---|
Gdawiec_Acceleretion_of_the_Robust_Newton_method.pdf | 4,72 MB | Adobe PDF | View/Open |
Items in RE-BUŚ are protected by copyright, with all rights reserved, unless otherwise indicated.