On developing a higher-order family of double-Newton methods with a bivariate weighting function

Young Hee Geum, Young Ik Kim and Beny Neta

Applied Mathematics and Computation, 2015, vol. 254, issue C, 277-290

Abstract: A high-order family of two-point methods costing two derivatives and two functions are developed by introducing a two-variable weighting function in the second step of the classical double-Newton method. Their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases. A variety of concrete numerical examples and relevant results are extensively treated to verify the underlying theoretical development. In addition, this paper investigates the dynamics of rational iterative maps associated with the proposed method and an existing method based on illustrated description of basins of attraction for various polynomials.

Keywords: Sixth-order convergence; Extraneous fixed point; Asymptotic error constant; Efficiency index; Double-Newton method; Basin of attraction (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:254:y:2015:i:c:p:277-290

DOI: 10.1016/j.amc.2014.12.130

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