{"title":"Of a Couple of Relaxation Iterative Methods Suited for Matrices of Bounded Linear Operators Defined over Banach Spaces","authors":"Samir Lemita, Mohammed Ghaith Mahcene","doi":"10.1142/s1793557123502030","DOIUrl":null,"url":null,"abstract":"By introducing matrices of linear bounded infinite-dimensional operators defined over some Banach spaces, and within the context of study, we make use of the definition of row strict diagonal dominance property to construct a generalization version of the Jacobi Under-Relaxation and the Successive Under-Relaxation iterative methods. The convergence analyses of the two new iterative methods are provided, and a numerical application to solve one Fredholm integral equation is presented to show the generalized methods’ effectiveness compared with their conventional opponents.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian-European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793557123502030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
By introducing matrices of linear bounded infinite-dimensional operators defined over some Banach spaces, and within the context of study, we make use of the definition of row strict diagonal dominance property to construct a generalization version of the Jacobi Under-Relaxation and the Successive Under-Relaxation iterative methods. The convergence analyses of the two new iterative methods are provided, and a numerical application to solve one Fredholm integral equation is presented to show the generalized methods’ effectiveness compared with their conventional opponents.
期刊介绍：
Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.
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