A New Hybrid Approach for Solving Large-scale Monotone Nonlinear Equations | Zendy

Jamilu Sabi’u | Zendy; Abdullah Shah | Zendy; Mohammed Yusuf Waziri | Zendy; Muhammad Kabir Dauda | Zendy

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A New Hybrid Approach for Solving Large-scale Monotone Nonlinear Equations

Author(s) -

Jamilu Sabi’u,

Abdullah Shah,

Mohammed Yusuf Waziri,

Muhammad Kabir Dauda

Publication year - 2020

Publication title -

journal of mathematical and fundamental sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.216

H-Index - 12

eISSN - 2337-5760

pISSN - 2338-5510

DOI - 10.5614/j.math.fund.sci.2020.52.1.2

Subject(s) - monotone polygon , conjugate gradient method , mathematics , convergence (economics) , nonlinear system , line search , nonlinear conjugate gradient method , scheme (mathematics) , scale (ratio) , projection (relational algebra) , derivation of the conjugate gradient method , mathematical optimization , conjugate residual method , gradient method , projection method , algorithm , computer science , mathematical analysis , gradient descent , geometry , dykstra's projection algorithm , artificial intelligence , artificial neural network , computer security , physics , radius , quantum mechanics , economics , economic growth

In this paper, a new hybrid conjugate gradient method for solving monotone nonlinear equations is introduced. The scheme is a combination of the Fletcher-Reeves (FR) and Polak-Ribiere-Polyak (PRP) conjugate gradient methods with the Solodov and Svaiter projection strategy. Using suitable assumptions, the global convergence of the scheme with monotone line search is provided. Lastly, a numerical experiment was used to enumerate the suitability of the proposed scheme for large-scale problems.

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