In this paper, a modified Newton-like method for nonlinear equations is proposed, which is based on a rational model. In the rational model, the Jacobian matrix is approximated by a matrix \(D_{k}\) which satisfies a new quasi-Newton equation. The new quasi-Newton equation exploits addition information by assuming a quadratic relationship between the information from the last three iterations. Under mild assumptions, the local convergence properties of the new method is presented. Numerical results illustrate that the modified Newton-like method is efficient.

中文翻译：

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非线性方程的改进的类牛顿法

本文提出了一种基于有理模型的改进的牛顿类非线性方程方法。在有理模型中，雅可比矩阵由满足新的拟牛顿方程的矩阵\（D_ {k} \）近似。新的拟牛顿方程通过假设来自最后三个迭代的信息之间的二次关系来利用加法信息。在温和的假设下，提出了新方法的局部收敛性。数值结果表明，改进的类牛顿法是有效的。