{"title":"Gradient neural network model for the system of two linear matrix equations and applications","authors":"Jelena Dakić , Marko D. Petković","doi":"10.1016/j.amc.2024.128930","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the new type of Gradient Neural Network (GNN) model is proposed for the following linear system of matrix equations: <span><math><mi>A</mi><mi>X</mi><mo>=</mo><mi>C</mi><mo>,</mo><mi>X</mi><mi>B</mi><mo>=</mo><mi>D</mi></math></span>. The convergence analysis of given models is shown. The model is applied for the computation of the regular matrix inverse, as well as Moore-Penrose and Drazin generalized inverses. Some illustrative examples and simulations are given to verify theoretical results.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"481 ","pages":"Article 128930"},"PeriodicalIF":3.4000,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324003916","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the new type of Gradient Neural Network (GNN) model is proposed for the following linear system of matrix equations: . The convergence analysis of given models is shown. The model is applied for the computation of the regular matrix inverse, as well as Moore-Penrose and Drazin generalized inverses. Some illustrative examples and simulations are given to verify theoretical results.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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