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Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations
Journal of the Egyptian Mathematical Society Pub Date : 2020-01-13 , DOI: 10.1186/s42787-019-0066-1
M. Koorapetse , P. Kaelo

In this paper, we propose a self adaptive spectral conjugate gradient-based projection method for systems of nonlinear monotone equations. Based on its modest memory requirement and its efficiency, the method is suitable for solving large-scale equations. We show that the method satisfies the descent condition F k T d k ≤ − c ∥ F k ∥ 2 , c > 0 $F_{k}^{T}d_{k}\leq -c\|F_{k}\|^{2}, c>0$ , and also prove its global convergence. The method is compared to other existing methods on a set of benchmark test problems and results show that the method is very efficient and therefore promising.

中文翻译:

求解非线性单调方程的自适应谱共轭梯度法

在本文中,我们提出了一种基于自适应谱共轭梯度的非线性单调方程系统的投影方法。基于其适度的内存需求和效率,该方法适用于求解大规模方程。我们证明该方法满足下降条件 F k T dk ≤ − c ∥ F k ∥ 2 , c > 0 $F_{k}^{T}d_{k}\leq -c\|F_{k}\| ^{2}, c>0$ ,也证明了它的全局收敛性。在一组基准测试问题上将该方法与其他现有方法进行比较,结果表明该方法非常有效,因此很有前景。
更新日期:2020-01-13
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