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Convergence Properties of an Iterative Method for Solving Symmetric Non-linear Equations

Author

Listed:
  • Weijun Zhou

    (Changsha University of Science and Technology)

  • Dongmei Shen

    (Changsha University of Science and Technology)

Abstract

We introduce an iterative method for solving symmetric systems of non-linear equations without computing Jacobian and gradient using the special structure of the underlying function. This derivative-free feature makes it solve relatively large-scale problems. We show that the proposed method has global and linear convergence properties under appropriate conditions. We also report some numerical results to show its efficiency.

Suggested Citation

  • Weijun Zhou & Dongmei Shen, 2015. "Convergence Properties of an Iterative Method for Solving Symmetric Non-linear Equations," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 277-289, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0547-1
    DOI: 10.1007/s10957-014-0547-1
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    Cited by:

    1. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    2. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.

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