Three-Term Hager–Zhang Projection Method for Monotone Nonlinear Equations
In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998 ) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed...
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| Published in: | Vietnam journal of mathematics Vol. 53; no. 1; pp. 109 - 130 |
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| Format: | Journal Article |
| Language: | English |
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01.01.2025
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| ISSN: | 2305-221X, 2305-2228 |
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| Abstract | In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369,
1998
) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed by Waziri et al. (Appl. Math. Comput.
361
, 645–660,
2019
), by extending its direction to three-term conjugate gradient direction. The proposed method has been shown to be globally convergent under some mild conditions. Numerical experiments show that the proposed method is effective and produces better results than some existing methods. |
|---|---|
| AbstractList | In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369,
1998
) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed by Waziri et al. (Appl. Math. Comput.
361
, 645–660,
2019
), by extending its direction to three-term conjugate gradient direction. The proposed method has been shown to be globally convergent under some mild conditions. Numerical experiments show that the proposed method is effective and produces better results than some existing methods. In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998) to solve monotone nonlinear equations is presented. The proposed method improved the numerical performance of the Hager–Zhang (HZ) method proposed by Waziri et al. (Appl. Math. Comput. 361, 645–660, 2019), by extending its direction to three-term conjugate gradient direction. The proposed method has been shown to be globally convergent under some mild conditions. Numerical experiments show that the proposed method is effective and produces better results than some existing methods. |
| Author | Majumder, Arunava Halilu, Abubakar Sani Murtala, Salisu Ahmed, Kabiru Waziri, Mohammed Yusuf |
| Author_xml | – sequence: 1 givenname: Abubakar Sani orcidid: 0000-0002-9680-266X surname: Halilu fullname: Halilu, Abubakar Sani email: abubakars.halilu@slu.edu.ng organization: Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Department of Mathematics, Sule Lamido University, Numerical Optimization Research Group, Bayero University – sequence: 2 givenname: Arunava surname: Majumder fullname: Majumder, Arunava organization: Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University – sequence: 3 givenname: Mohammed Yusuf surname: Waziri fullname: Waziri, Mohammed Yusuf organization: Numerical Optimization Research Group, Bayero University, Department of Mathematical Sciences, Bayero University – sequence: 4 givenname: Kabiru surname: Ahmed fullname: Ahmed, Kabiru organization: Numerical Optimization Research Group, Bayero University, Department of Mathematical Sciences, Bayero University – sequence: 5 givenname: Salisu surname: Murtala fullname: Murtala, Salisu organization: Numerical Optimization Research Group, Bayero University, Department of Mathematics, Federal University |
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| Cites_doi | 10.1007/s40324-020-00228-9 10.1016/j.matcom.2021.03.020 10.1016/0041-5553(69)90035-4 10.1142/S0219876220500437 10.1080/10556788.2013.833199 10.1090/S0025-5718-1974-0343581-1 10.1080/02331934.2014.938072 10.1137/S1052623497318992 10.1007/s101070100263 10.1093/comjnl/7.2.149 10.1007/978-1-4757-6388-1_18 10.1007/s002450010019 10.1016/j.apnum.2020.02.017 10.1080/02331934.2020.1808647 10.14419/ijamr.v6i4.8072 10.1007/s11590-014-0736-8 10.6028/jres.049.044 10.1007/s11075-018-0541-z 10.1007/s40065-019-0264-6 10.1016/j.camwa.2015.09.014 10.1016/j.camwa.2006.12.081 10.1137/030601880 10.1016/j.jmaa.2013.04.017 10.2306/scienceasia1513-1874.2014.40.295 10.19139/soic-2310-5070-532 10.1186/s13660-016-1239-1 10.1080/10556788.2017.1338288 10.1007/s40314-021-01624-1 10.1155/2019/5976595 10.1137/S0036142998335704 |
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| Keywords | Conjugate gradient method Primary 65K05 90C53 Hager–Zhang parameter Global convergence Numerical experiment Secondary 90C30 Monotone nonlinear equations |
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| Snippet | In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369,
1998
) to... In this paper, a conjugate gradient method combined with the projection technique of Solodov and Svaiter (Kluwer Academic Publishers, pp. 355–369, 1998) to... |
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| SubjectTerms | Algorithms Conjugate gradient method Mathematics Mathematics and Statistics Methods Nonlinear equations Optimization Original Article Value analysis |
| Title | Three-Term Hager–Zhang Projection Method for Monotone Nonlinear Equations |
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