Title: Polynomiography for square systems of equations with Mann and Ishikawa iterations
Authors: Gdawiec, Krzysztof
Kotarski, Wiesław
Lisowska, Agnieszka
Citation: WSCG '2016: short communications proceedings: The 24th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2016 in co-operation with EUROGRAPHICS: University of West Bohemia, Plzen, Czech RepublicMay 30 - June 3 2016, p. 1-5.
Issue Date: 2016
Publisher: Václav Skala - UNION Agency
Document type: konferenční příspěvek
URI: wscg.zcu.cz/WSCG2016/!!_CSRN-2602.pdf
ISBN: 978-80-86943-58-9
ISSN: 2464-4617
Keywords: Mannova iterace;Ishikawova iterace;polynomiografie;počítačová grafika
Keywords in different language: Mann iteration;Ishikawa iteration;polynomiography;computer graphics
Abstract: In this paper we propose to replace the standard Picard iteration in the Newton–Raphson method by Mann and Ishikawa iterations. This iteration’s replacement influence the solution finding process that can be visualized as polynomiographs for the square systems of equations. Polynomiographs presented in the paper, in some sense, are generalization of Kalantari’s polynomiography from a single polynomial equation to the square systems of equations. They are coloured based on two colouring methods: basins of attractions with different colours for every real root and colouring dependent on the number of iterations. Possible application of the presented method can be addressed to computer graphics where aesthetic patterns can be used in e.g. texture generation, animations, tapestry design.
Rights: © Václav Skala - UNION Agency
Appears in Collections:WSCG '2016: Short Papers Proceedings

Files in This Item:
File Description SizeFormat 
Gdawiec.pdfPlný text448,5 kBAdobe PDFView/Open

Please use this identifier to cite or link to this item: http://hdl.handle.net/11025/29681

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.