Syahmi Afandi Sariman1, Ishak Hashim1, *
CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 69-85, 2020, DOI:10.32604/cmc.2020.010836
- 23 July 2020
Abstract The classical iterative methods for finding roots of nonlinear equations, like
the Newton method, Halley method, and Chebyshev method, have been modified
previously to achieve optimal convergence order. However, the Householder method has
so far not been modified to become optimal. In this study, we shall develop two new
optimal Newton-Householder methods without memory. The key idea in the
development of the new methods is the avoidance of the need to evaluate the second
derivative. The methods fulfill the Kung-Traub conjecture by achieving optimal
convergence order four with three functional evaluations and order eight with More >
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