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An improved spectral conjugate gradient projection method for monotone nonlinear equations with application

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Abstract

In this paper, we propose an enhanced spectral conjugate gradient (CG) projection method for solving monotone nonlinear equations with application in signal processing. The derivation of the CG parameter involves a combination of the quasi-Newton and the CG search directions, respectively. This integration aims to harness the efficiency of the quasi-Newton direction and the global convergence properties of the CG method, resulting in a more versatile and efficient algorithm. The search direction ensures sufficient descent without relying on any line search, and the global convergence of the proposed method is established under certain conditions. Numerical experiments have been conducted to evaluate the effectiveness of the proposed method. Finally, the proposed method has been applied to address the problems arising in signal reconstruction.

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Acknowledgements

The first author intends to convey his appreciation to Professor Peng Jun for the guidance, counsel, and assistance extended during this research. The third author wishes to express gratitude to the Department of Mathematics and Applied Mathematics, Central South University, Changsha, Hunan, China.

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Authors and Affiliations

  1. School of Mathematics and Statistics, HNP-LAMA Central South University Changsha, Hunan, 410083, China

    Sadiq Bashir Salihu & Muhammad Abdullahi

  2. Department of Mathematics, Sule Lamido University, Kafin-Hausa, Nigeria

    Abubakar Sani Halilu & Muhammad Abdullahi

  3. Department of Mathematics, School of Science, Jigawa State College of Education Gumel, Gumel, Nigeria

    Sadiq Bashir Salihu

  4. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Kabiru Ahmed

  5. Department of Mathematics, Federal University Dutse, Jigawa, Nigeria

    Salisu Murtala

  6. Department of Mathematics, Mewar University India, NH-48 Gangrar chittorgarh, Rajasthan, 312901, India

    Sadiq Bashir Salihu & Pramod Mehta

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  1. Sadiq Bashir Salihu
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  2. Abubakar Sani Halilu
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  3. Muhammad Abdullahi
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  4. Kabiru Ahmed
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  5. Pramod Mehta
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  6. Salisu Murtala
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Correspondence to Sadiq Bashir Salihu.

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Salihu, S.B., Halilu, A.S., Abdullahi, M. et al. An improved spectral conjugate gradient projection method for monotone nonlinear equations with application. J. Appl. Math. Comput. 70, 3879–3915 (2024). https://doi.org/10.1007/s12190-024-02121-4

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  • DOI: https://doi.org/10.1007/s12190-024-02121-4

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