A class of iterative methods for solving nonlinear projection equations
Journal of Optimization Theory and Applications
Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
Some modification of Newton's method by the method of undetermined coefficients
Computers & Mathematics with Applications
Three-step iterative methods with optimal eighth-order convergence
Journal of Computational and Applied Mathematics
Finding the solution of nonlinear equations by a class of optimal methods
Computers & Mathematics with Applications
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This paper presents an improvement of the sixth-order method of Chun and Neta as a class of three-step iterations with optimal efficiency index, in the sense of Kung-Traub conjecture. Each member of the presented class reaches the highest possible order using four functional evaluations. Error analysis will be studied and numerical examples are also made to support the theoretical results. We then present results which describe the dynamics of the presented optimal methods for complex polynomials. The basins of attraction of the existing optimal methods and our methods are presented and compared to illustrate their performances.