A modified prp-cg type derivative-free algorithm with optimal choices for solving large-scale nonlinear symmetric equations

Jamilu Sabi’u, Kanikar Muangchoo*, Abdullah Shah, Auwal Bala Abubakar, Lateef Olakunle Jolaoso

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with the default Newton direction. In addition, the corresponding PRP parameters are incorporated with the Li and Fukushima approximate gradient to propose two robust CG-type algorithms for finding solutions for large-scale systems of symmetric nonlinear equations. We have also demonstrated the global convergence of the suggested algorithms using some classical assumptions. Finally, we demonstrated the numerical advantages of the proposed algorithms compared to some of the existing methods for nonlinear symmetric equations.

Original languageEnglish
Article number234
Pages (from-to)1-15
Number of pages15
JournalSymmetry
Volume13
Issue number2
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Approximate gradient
  • Measure function
  • Newton direction
  • Symmetric systems

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