{"title":"基于梯度的复共轭矩阵与转置矩阵耦合迭代算法","authors":"H. Yin, Huamin Zhang","doi":"10.4236/alamt.2021.113007","DOIUrl":null,"url":null,"abstract":"Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.","PeriodicalId":65610,"journal":{"name":"线性代数与矩阵理论研究进展(英文)","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations\",\"authors\":\"H. Yin, Huamin Zhang\",\"doi\":\"10.4236/alamt.2021.113007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.\",\"PeriodicalId\":65610,\"journal\":{\"name\":\"线性代数与矩阵理论研究进展(英文)\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"线性代数与矩阵理论研究进展(英文)\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.4236/alamt.2021.113007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"线性代数与矩阵理论研究进展(英文)","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4236/alamt.2021.113007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations
Gradient-based iterative algorithm is suggested for solving a coupled complex conjugate and transpose matrix equations. Using the hierarchical identification principle and the real representation of a complex matrix, a convergence proof is offered. The necessary and sufficient conditions for the optimal convergence factor are determined. A numerical example is offered to validate the efficacy of the suggested algorithm.
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