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Title: Higher Order Methods of the Basic Family of Iterations via S-Iteration Scheme with s-Convexity
Authors: Gdawiec, Krzysztof
Shahid, Abdul Aziz
Waqas, Nazeer
Keywords: root finding; s-iteration; s-convexity; polynomiography
Issue Date: 2020
Citation: "Mediterranean Journal of Mathematics" Vol. 17, art. no 43
Abstract: There are many methods for solving a polynomial equation and many different modifications of those methods have been proposed in the literature. One of such modifications is the use of various iteration processes taken from the fixed point theory. In this paper, we propose a modification of the iteration processes used in the Basic Family of iterations by replacing the convex combination with an s-convex one. In our study, we concentrate only on the S-iteration with s-convexity. We present some graphical examples, the so-called polynomiographs, and numerical experiments showing the dependency of polynomiograph’s generation time on the value of the s parameter in the s-convex combination.
DOI: 10.1007/s00009-020-1491-y
ISSN: 1660-5446
Appears in Collections:Artykuły (WNŚiT)

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