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On the efficiency index of one-point iterative processes

机译:关于单点迭代过程的效率指标

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In this paper, we analyze the index of efficiency of one-point iterative processes, which are in practice the most used methods to solve a nonlinear equation. We obtain the best situation for one-point iterative processes with cubic convergence: Chebyshev’s method, Halley’s method, the super-Halley method and many others classical iterative methods with order of convergence three. By means of a construction of particular multipoint iterations, we get to improve the best situation obtained for one-point methods. Moreover, these type of multipoint iterations, can be considered as quasi-one-point iterations, since they only depend on one initial approximation. Numerical examples are given and the computed results support this theory.
机译:在本文中,我们分析了单点迭代过程的效率指标,这是实际上求解非线性方程的最常用方法。对于三次收敛的单点迭代过程,我们获得了最佳的情况:切比雪夫方法,哈雷方法,超级哈利方法以及许多其他具有收敛顺序的经典迭代方法。通过构造特定的多点迭代,我们可以改善单点方法获得的最佳情况。而且,这些类型的多点迭代可被视为准单点迭代,因为它们仅依赖于一个初始近似值。给出了算例,计算结果支持了这一理论。

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