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Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations
Applied Numerical Mathematics ( IF 2.8 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.apnum.2020.02.017
Jamilu Sabi'u , Abdullah Shah , Mohammed Yusuf Waziri

Abstract We derived two adaptive choices for the nonnegative parameter of the Hager-Zhang conjugate gradient method. The first was achieved by minimizing the Frobenius condition number of the search direction matrix and the other by minimizing the difference between the smallest and the largest singular value. Global convergence is based on an appropriate assumption. Preliminary numerical results demonstrate the efficiency of the two adaptive choices.

中文翻译:

求解单调非线性方程的两种最优Hager-Zhang共轭梯度法

摘要 我们为Hager-Zhang共轭梯度法的非负参数推导出了两种自适应选择。第一个是通过最小化搜索方向矩阵的 Frobenius 条件数来实现的,另一个是通过最小化最小和最大奇异值之间的差异来实现的。全局收敛基于适当的假设。初步数值结果证明了两种自适应选择的效率。
更新日期:2020-07-01
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