An acceleration of Newton's method: Super-Halley method
Applied Mathematics and Computation
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
Recurrence relations for a Newton-like method in Banach spaces
Journal of Computational and Applied Mathematics
Revisit of Jarratt method for solving nonlinear equations
Numerical Algorithms
Semilocal convergence of a sixth-order Jarratt method in Banach spaces
Numerical Algorithms
Semilocal convergence of a sixth-order method in Banach spaces
Numerical Algorithms
Semilocal convergence and R-order for modified Chebyshev-Halley methods
Numerical Algorithms
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In this paper, we study a variant of the super-Halley method with fourth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived and then an existence-uniqueness theorem is given to establish the R-order of the method to be four and a priori error bounds. Finally, some numerical applications are presented to demonstrate our approach.