{"title":"两个线性矩阵方程组的梯度神经网络模型及其应用","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":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-07-14\",\"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\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","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":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Gradient neural network model for the system of two linear matrix equations and applications
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
