{"title":"A New Hybrid Approach for Solving Large-scale Monotone Nonlinear Equations","authors":"J. Sabi’u, A. Shah, M. Waziri, M. K. Dauda","doi":"10.5614/j.math.fund.sci.2020.52.1.2","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":16255,"journal":{"name":"Journal of Mathematical and Fundamental Sciences","volume":"18 1","pages":"17-26"},"PeriodicalIF":0.5000,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical and Fundamental Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5614/j.math.fund.sci.2020.52.1.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 7
Abstract
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.
期刊介绍：
Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health Sciences, Medical Sciences, Pharmacy), Mathematics, Physics, and Statistics. New submissions of mathematics articles starting in January 2020 are required to focus on applied mathematics with real relevance to the field of natural sciences. Authors are invited to submit articles that have not been published previously and are not under consideration elsewhere.
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