A nonmonotone PRP conjugate gradient method for solving square and under-determined systems of equations

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• 作者：D. Ataee Tarzanagh^a ; ^{Tarzanagh@ufl.edu} ; P. Nazari^b ; ^{p.nazari17@gmail.com} ; M. Reza Peyghami^c ; ^d ; ^{peyghami@kntu.ac.ir}
• 关键词：PRP conjugate gradient method ; Nonmonotone line search ; Nonlinear systems of equations ; Derivative-free methods
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：339-354
• 全文大小：872 K
• 卷排序：73

文摘

In this paper, we propose a new derivative-free preconditioned conjugate gradient method in order for solving large-scale square and under-determined nonlinear systems of equations. The proposed method is also equipped with a relaxed nonmonotone line search technique. Under some suitable assumptions, the global convergence property is established. Numerical results on some square and under-determined test systems show the efficiency and effectiveness of the new method in practice. An application of the new method for solving nonlinear integro-differential equations is also provided.