A Simple Conjugate Gradient Type Method for Solving Large-scale Systems of Nonlinear Equations


  • M K Dauda Department of Mathematical Sciences, Kaduna State University, Nigeria
  • A S Magaji Department of Mathematical Sciences, Kaduna State University, Nigeria.
  • U S Shehub Department of Mathematics and Statistics, Kaduna Polytechnic, Kaduna Nigeria
  • M A Usman Department of Computer Sciences, Shehu Idris College of Health Science and Technology, Kaduna Nigeria
  • M Y Waziri Department of Mathematical Sciences, Bayero University, Kano, Nigeria




Conjugate Gradient, Broydens Update, Global Convergence, Nonlinear Equations, Approximations



Quasi Newton’s method is among the most promising algorithm for solving systems of nonlinear equations. In this family, Broyden’s method update is the famous. This paper presents a simple conjugate gradient (CG) method for solving large-scale systems of nonlinear equations via memoryless Broyden’s approach. The attractive attribute of this method is due to its low memory requirements, global convergence properties and simple implementation. Under suitable conditions, the proposed method converges globally. Numerical performance of the proposed method are compared with the well-known conjugate gradients (CG) methods using benchmarks problems. The report demonstrate that the proposed method is reliable, efficient and competitive.