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Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations

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Abstract

We present a derivative-free diagonal Polak–Ribière–Polyak like algorithm for solving large-scale systems of nonlinear equations. The search direction of the algorithm is obtained by incorporating a positive definite diagonal matrix with the positive Polak–Ribière–Polyak (PRP+) parameter. By employing a derivative-free line search technique, the global convergence and convergence rate of the algorithm are achieved. Numerical experiments performed on some large-scale systems of nonlinear equations demonstrated the good performance of the algorithm.

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Acknowledgements

The authors would like to thank the reviewers and the Editor-in-Chief for their constructive suggestions which improved the earlier version of this paper.

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Correspondence to Hassan Mohammad.

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The MATLAB codes for the implementation of the dprp+ algorithm are available upon request. The datasets used to plot the graphs presented in Section 4 of this paper are openly available in the corresponding author’s repository https://acrobat.adobe.com/link/track?uri=urn:aaid:scds:US:ac15dc9a-b04b-437a-b978-ca36960e0f9e.

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Mohammad, H., Awwal, A.M. Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations. Numer Algor 91, 1441–1460 (2022). https://doi.org/10.1007/s11075-022-01309-8

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  • DOI: https://doi.org/10.1007/s11075-022-01309-8

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