A deformed Jarratt's method for solving non-linear equation in Banach space

Xufeng Shang, Yubo Yuan
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Abstract

In this paper, a deformed Jarratt's iteration without the inverse of the derivative is presented firstly and the convergence theorem of this method is established by using majoring functions. The new method does not required the evaluation of the inverse of derivative, and it achieves the fourth order. Finally, illustrative examples are included to demonstrate the validity and applicability of the technique.
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求解Banach空间非线性方程的一种变形Jarratt方法
本文首先给出了一种无导数逆的变形Jarratt迭代,并利用主要函数建立了该方法的收敛性定理。该方法不需要求导数的逆,可以达到四阶。最后,通过实例说明了该方法的有效性和适用性。
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