A quasi-Newton algorithm for large-scale nonlinear equations
 作者： Linghua Huang 作者单位： 1School of Information and Statistics, Guangxi University of Finance & Economics 刊名： Journal of Inequalities and Applications, 2017, Vol.2017 (1), pp.1-16 来源数据库： Springer Journal DOI： 10.1186/s13660-017-1301-7 关键词： nonlinear equations;  large-scale;  conjugate gradient;  quasi-Newton method;  global convergence; 英文摘要： Abstract(#br)In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i) a conjugate gradient (CG) algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii) a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the ... FileRef="13660_2017_1301_Article_IEq2.gif" Format="GIF" Rendition="HTML" Type="Linedraw"/> 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

• large　大的
• nonlinear　非线性的
• scale　度盘
• Newton　牛顿
• algorithm　算法
• quasi