The present paper describes the study of semilocal convergence of seventh-order iterative method, in Banach spaces for solving nonlinear equations. The existence and uniqueness results have been verified followed by error bounds. It is also discussed that the considered scheme has not only the higher convergence order but also improved computational efficiency, which is the significant issue when dealing the nonlinear system problems. The theoretical development has been justified by applying it to a numerical problem.

中文翻译：

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Banach空间中七阶方法的半局部收敛及其计算效率

本文介绍了在Banach空间中求解非线性方程组的七阶迭代方法的半局部收敛性的研究。存在性和唯一性结果已得到验证，其后是误差范围。还讨论了所考虑的方案不仅具有更高的收敛阶而且还提高了计算效率，这是解决非线性系统问题时的重要问题。通过将其应用于数值问题已经证明了理论的发展。