Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional evaluations per step, and hence is optimal in the sense of Kung-Traub conjecture. Moreover, in order to have additional information to choose some elements of the class, in particular some stable enough,  use complex dynamics tools to analyze their stability. Then, some ranges of values of the parameter are found to be avoided but  show that the region of stable members of this family is vast. It is found by way of illustration that these proposed methods are very useful in high precision computations.
['Alicia Cordero', 'Munish Kansal', 'Vinay Kanwar', 'Juan R. Torregrosa']
I am writing a research paper on a idea A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence
[{"from": "human", "value": "I am writing a research paper on a idea A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional evaluations per step, and hence is optimal in the sense of Kung-Traub conjecture. Moreover, in order to have additional information to choose some elements of the class, in particular some stable enough,  use complex dynamics tools to analyze their stability. Then, some ranges of values of the parameter are found to be avoided but  show that the region of stable members of this family is vast. It is found by way of illustration that these proposed methods are very useful in high precision computations."}]