Abstract
Recently, the pseudo-Newton method was proposed to solve the problem of finding the points for which the maximal modulus of a given polynomial over the unit disk is attained. In this paper, we propose a modification of this method, which relies on the use of fractional order derivatives. The proposed modification is evaluated twofold: visually via polynomiographs coloured according to the number of iterations, and numerically by using the convergence area index, the average number of iterations and generation time of polynomiographs. The experimental results show that the fractional pseudo-Newton method for some fractional orders behaves better in comparison to the standard algorithm.
W. Kotarski—Independent Researcher.
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Gdawiec, K., Lisowska, A., Kotarski, W. (2022). Pseudo-Newton Method with Fractional Order Derivatives. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13351. Springer, Cham. https://doi.org/10.1007/978-3-031-08754-7_22
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