An Optimally Convergent Three-step Class of Derivative-free Methods
نویسنده
چکیده
In this paper, a new optimally convergent eighth-order class of three-step without memory methods is suggested. We here pursue derivative-free algorithms, i.e., algorithms requiring only the ability to evaluate the (objective) function. Since the types of problems that these algorithms can solve are extremely diverse in nature. The analysis of convergence shows that each derivative-free method of our class requires four pieces of information per full iteration to obtain the optimal efficiency index 1.682. Numerical experiments with comparison to some existing derivative-free methods are furnished to support the underlying theory. AMS classification: 65H05 • 65B99 • 41A25
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