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Descent Perry conjugate gradient methods for systems of monotone nonlinear equations

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Abstract

In this paper, we present a family of Perry conjugate gradient methods for solving large-scale systems of monotone nonlinear equations. The methods are developed by combining modified versions of Perry (Oper. Res. Tech. Notes 26(6), 1073–1078, 1978) conjugate gradient method with the hyperplane projection technique of Solodov and Svaiter (1998). Global convergence and numerical results of the methods are established and preliminary numerical results shows that the proposed methods are promising and more effective compared to some existing methods in the literature.

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The authors would like to thank the anonymous reviewers for their helpful comments and suggestions which improved the quality of the paper.

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Waziri, M.Y., Hungu, K.A. & Sabi’u, J. Descent Perry conjugate gradient methods for systems of monotone nonlinear equations. Numer Algor 85, 763–785 (2020). https://doi.org/10.1007/s11075-019-00836-1

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