{'fraction_non_alphanumeric': 0.02009273570324575, 'fraction_numerical': 0.0, 'mean_word_length': 5.171428571428572, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
SOME MODIFICATIONS OF CHEBYSHEV-HALLEY’S METHODS FREE FROM SECOND DERIVATIVE WITH EIGHTH-ORDER OF CONVERGENCE

The variant of Chebyshev-Halley’s method is an iterative method used for solving a nonlinear equation with third order of convergence. In this paper, we present some new variants of three steps Chebyshev-Halley’s method free from second derivative with two parameters. The proposed methods have eighth-order of convergence for  and  and require four evaluations of functions per iteration with index efficiency equal to . Numerical simulation will be presented by using several functions to show the performance of the proposed methods.