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Finite Difference Newton's method for systems of nonlinear equations

机译：非线性方程组的有限差分牛顿法

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摘要

Finite difference Newton's method is the one point iteration scheme introduced by Weerakoon (1996) to approximate single roots of nonlinear equations. Proposed scheme replaces The derivative of the function in Newton's method by appropriately chosen forward or backward Difference formulae. In this paper the same method is applied to functions of two variables. It is Proved that the method is second order conergent. Computational evidence provided here not only Supports the theory but goes beyond that, suggesting it is not necessary to have the initial quess within A sufficiently close neighbourhood for the convergence of the proposed method. As problems, such As looping which effect Newton's method, can be overcome with the proposed method by choosing Suitable stepsizes, finite difference Newton's method provides convergent results even for functions Which do not converge with Newton's iterations.
机译：有限差分牛顿法是Weerakoon（1996）引入的单点迭代方案，用于近似非线性方程的单根。建议方案通过适当选择正向或反向差分公式来代替牛顿方法中的函数导数。本文将相同的方法应用于两个变量的函数。证明该方法是二阶收敛的。这里提供的计算证据不仅支持该理论，而且还支持该理论，这表明在A足够近的邻域内具有初始问题对于所提出方法的收敛是不必要的。通过选择合适的步长可以解决所提出的方法所产生的问题，例如影响牛顿方法的循环，即使牛顿迭代不收敛的函数，有限差分牛顿方法也能提供收敛的结果。

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