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

Ataee Tarzanagh, D ; Sharif University of Technology | 2017

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  1. Type of Document: Article
  2. DOI: 10.1016/j.camwa.2016.11.026
  3. Publisher: Elsevier Ltd , 2017
  4. Abstract:
  5. 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. © 2016 Elsevier Ltd
  6. Keywords:
  7. Derivative-free methods ; Nonlinear systems of equations ; Nonmonotone line search ; PRP conjugate gradient method ; Differential equations ; Integrodifferential equations ; Nonlinear equations ; Nonlinear systems ; Numerical methods ; Global convergence properties ; Non-linear integro-differential equations ; Non-linear systems of equations ; Numerical results ; Preconditioned conjugate gradient method ; Systems of equations ; Conjugate gradient method
  8. Source: Computers and Mathematics with Applications ; Volume 73, Issue 2 , 2017 , Pages 339-354 ; 08981221 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0898122116306587