This paper presents the two-parameter scaling memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi-Newton method for ill-conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method. Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results.

中文翻译：

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用于求解单调非线性方程组的无导数标度无记忆 Broyden-Fletcher-Goldfarb-Shanno 方法

本文介绍了用于求解单调非线性方程组的双参数缩放无记忆 Broyden-Fletcher-Goldfarb-Shanno (BFGS) 方法。缩放参数的最优值是通过最小化涉及无记忆BFGS矩阵的所有特征值的度量函数来获得的。最优值可用于病态矩阵的拟牛顿法分析。该算法也可以描述为投影技术和无记忆BGFS方法的结合。提供了该方法的全局收敛。为了验证和提高方案的效率，计算了一些测试问题并与现有结果进行了比较。