Skip navigation

Please use this identifier to cite or link to this item: http://hdl.handle.net/20.500.12128/3238
Title: Polynomiography for the Polynomial Infinity Norm via Kalantari's Formula and Nonstandard Iterations
Authors: Gdawiec, Krzysztof
Kotarski, Wiesław
Keywords: fractals; polynomiography; iterations; root finding
Issue Date: 2017
Citation: Applied Mathematics and Computation, Vol. 307 (2017), s. 17-30
Abstract: In this paper, an iteration process, referred to in short as MMP, will be considered. This iteration is related to finding the maximum modulus of a complex polynomial over a unit disc on the complex plane creating intriguing images. Kalantari calls these images polynomiographs independently from whether they are generated by the root finding or maximum modulus finding process applied to any polynomial. We show that the images can be easily modified using different MMP methods (pseudo-Newton, MMP-Householder, methods from the MMP-Basic, MMP-Parametric Basic or MMP-Euler-Schroder Families of Iterations) with various kinds of non-standard iterations. Such images are interesting from three points of views: scientific, educational and artistic. We present the results of experiments showing automatically generated non-trivial images obtained for different modifications of root finding MMP-methods. The colouring by iteration reveals the dynamic behaviour of the used root finding process and its speed of convergence. The results of the present paper extend Kalantari's recent results in finding the maximum modulus of a complex polynomial based on Newton's process with the Picard iteration to other MMP-processes with various non-standard iterations.
URI: http://hdl.handle.net/20.500.12128/3238
DOI: 10.1016/j.amc.2017.02.038
ISSN: 0096-3003
Appears in Collections:Artykuły (WINOM)

Files in This Item:
File Description SizeFormat 
Gdawiec_Polynomiography_for_the_polynomial_infinity_norm.pdf3,56 MBAdobe PDFView/Open
Show full item record


Uznanie autorstwa - użycie niekomercyjne, bez utworów zależnych 3.0 Polska Creative Commons License Creative Commons