 A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed pointsYoung Hee Geum, Young Ik Kim and Beny Neta Applied Mathematics and Computation, 2016, vol. 283, issue C, 120-140 Abstract: A class of three-point sixth-order multiple-root finders and the dynamics behind their extraneous fixed points are investigated by extending modified Newton-like methods with the introduction of the multivariate weight functions in the intermediate steps. The multivariate weight functions dependent on function-to-function ratios play a key role in constructing higher-order iterative methods. Extensive investigation of extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments applied to a number of test equations strongly support the underlying theory pursued in this paper. Relevant dynamics of the proposed methods is well presented with a variety of illustrative basins of attraction applied to various test polynomials. Keywords: Multiple-zero finder; Extraneous fixed point; Modified Newton’s method; Basins of attraction (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:283:y:2016:i:c:p:120-140 DOI: 10.1016/j.amc.2016.02.029 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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