Abstract
In this article, we introduce a unified approach to constructing a higher-order derivative-free scheme based on the approximations of F'(zk)-1. A family of order p=6,7 derivative-free method is proposed and compared to some well-known methods. The necessary and sufficient condition for p-th order of convergence are given in terms of parameter matrices τ(k) and α(k) . Some good choices of and are offered. Numerical experiments were carried out to confirm the theoretical results.
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