{"title":"A Levenberg–Marquardt type algorithm with a Broyden-like update technique for solving nonlinear equations","authors":"Jingyong Tang , Jinchuan Zhou","doi":"10.1016/j.cam.2024.116401","DOIUrl":null,"url":null,"abstract":"<div><div>We propose a variant Broyden-like method for solving nonlinear equations. At each iteration, the proposed method solves a Levenberg–Marquardt type equation in which the matrix is updated by the Broyden-like formula. The global convergence ensured by a nonmonotone derivative-free line search is proved without the nonsingularity condition. Moreover, the proposed method has local quadratic convergence under suitable conditions. Numerical experiments show that our method is more effective than the traditional Broyden-like method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116401"},"PeriodicalIF":2.1000,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006496","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a variant Broyden-like method for solving nonlinear equations. At each iteration, the proposed method solves a Levenberg–Marquardt type equation in which the matrix is updated by the Broyden-like formula. The global convergence ensured by a nonmonotone derivative-free line search is proved without the nonsingularity condition. Moreover, the proposed method has local quadratic convergence under suitable conditions. Numerical experiments show that our method is more effective than the traditional Broyden-like method.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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