Some modifications of Newton’s method with fifth-order convergence. (English) Zbl 1130.41005

Summary: We present some new modifications of Newton’s method for solving nonlinear equations. Analysis of convergence shows that these methods have order of convergence five. Numerical tests verifying the theory are given and based on these methods, a class of new multistep iterations is developed.


41A25 Rate of convergence, degree of approximation
65D99 Numerical approximation and computational geometry (primarily algorithms)
Full Text: DOI


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