Optimal Order of One-Point and Multipoint Iteration
Journal of the ACM (JACM)
Numerical Analysis
Computers & Mathematics with Applications
Optimal Steffensen-type methods with eighth order of convergence
Computers & Mathematics with Applications
Finding the solution of nonlinear equations by a class of optimal methods
Computers & Mathematics with Applications
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The calculation of derivatives of a function mostly takes up a great deal of time and even in some cases, such as the existing problems in engineering and optimization, is impossible to be evaluated directly. Accordingly, an accurate derivative-free class of three-step methods is suggested for solving f(x) = 0. The proposed three-step technique comprises four evaluations of the function per iteration. The analytical proof of the main contribution is given. And finally, the accuracy of the developed techniques is tested numerically by solving numerical examples.