{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T07:13:13Z","timestamp":1779001993853,"version":"3.51.4"},"reference-count":88,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["075-15-2022-1121"],"award-info":[{"award-number":["075-15-2022-1121"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.<\/jats:p>","DOI":"10.3390\/a16020064","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T05:06:14Z","timestamp":1674104774000},"page":"64","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0655-3741","authenticated-orcid":false,"given":"Predrag S.","family":"Stanimirovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia"},{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bilall I.","family":"Shaini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Sciences, State University of Tetova, St. Ilinden, n.n., 1220 Tetovo, North Macedonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jamilu","family":"Sabi\u2019u","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yusuf Maitama Sule University, Kano 700282, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5073-143X","authenticated-orcid":false,"given":"Milena J.","family":"Petrovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9179-0965","authenticated-orcid":false,"given":"Branislav","family":"Ivanov","sequence":"additional","affiliation":[{"name":"Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210 Bor, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinwei","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Business, Jiangnan University, Lihu Blvd, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alena","family":"Stupina","sequence":"additional","affiliation":[{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Prosp. 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