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Improved conjugate gradient method for nonlinear system of equations

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Abstract

In this paper, we propose a hybrid conjugate gradient (CG) method based on the approach of convex combination of Fletcher–Reeves (FR) and Polak–Ribière–Polyak (PRP) parameters, and Quasi-Newton’s update. This is made possible by using self-scaling memory-less Broyden’s update together with a hybrid direction consisting of two CG parameters. However, an important property of the new algorithm is that, it generates a descent search direction via non-monotone type line search. The global convergence of the algorithm is established under appropriate conditions. Finally, numerical experiments on some benchmark test problems, demonstrate the effectiveness of the proposed algorithm over some existing alternatives.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria

    Mohammed Yusuf Waziri & Auwal Bala Abubakar

  2. Department of Sciences, School of Continuing Education, Bayero University, Kano, Nigeria

    Aliyu Yusuf

Authors
  1. Mohammed Yusuf Waziri
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  2. Aliyu Yusuf
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  3. Auwal Bala Abubakar
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Correspondence to Mohammed Yusuf Waziri.

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Communicated by Andreas Fischer.

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Waziri, M.Y., Yusuf, A. & Abubakar, A.B. Improved conjugate gradient method for nonlinear system of equations. Comp. Appl. Math. 39, 321 (2020). https://doi.org/10.1007/s40314-020-01374-6

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  • DOI: https://doi.org/10.1007/s40314-020-01374-6

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