非线性系统的多元谱杂交HS和PRP方法
A multivariate spectral hybridization of HS and PRP method for nonlinear systems of equations
摘要：
提出了一种求解大规模非线性系统的Hestenes-Stiefel（HS）和Polak-Ribiere-Polyak（PRP）的多元谱杂交方法.该方法的搜索方向是通过将多元光谱方法与Hestenes-Stiefel和Polak-Ribiere-Polyak参数的正杂交（HS & PRP混合+）来获得的。通过采用无导数的非单调线搜索技术，证明了该方法产生的序列的整体收敛性。数值实验表明，与文献中设计的求解大规模非线性系统的方法相比，该方法具有良好的性能。
英文摘要：
We present a multivariate spectral hybridization of Hestenes-Stiefel (HS) and Polak-Ribiere-Polyak (PRP) method for solving large-scale nonlinear systems of equations. The search direction of the method is obtained by incorporating a multivariate spectral approach with the positive hybridization of Hestenes-Stiefel and Polak-Ribiere-Polyak parameters (HS & PRP hybrid+). By employing a derivative-free nonmonotone line search technique, the global convergence of the sequence generated by the method is proven. Numerical experiments are given to demonstrate the good performance of the method compared with similar methods in the literature designed for solving large-scale nonlinear systems of equations.
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