{"title":"解决矩阵方程 $${\\varvec{A}\\boldsymbol{ Z}-\\overline{boldsymbol{ Z}}{\\varvec{B}}={\\varvec{C}}$ 的加速雅各比梯度迭代算法","authors":"Ahmed M. E. Bayoumi","doi":"10.1007/s40995-024-01629-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present an accelerated Jacobi-gradient-based iterative AJGI algorithm to solve the matrix equation <span>\\(A{ Z}-\\overline{ Z}B=C\\)</span>, which is based on algorithms presented by Bayoumi (Appl Math Inf Sci, 2021). The iterative solution converges to the exact solution for any initial value under appropriate assumptions. Numerical examples are provided to support the suggested approach and verify its effectiveness and accuracy when compared to a recent one previously described in Bayoumi (Appl Math Inf Sci, 2021).</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"48 3","pages":"659 - 666"},"PeriodicalIF":1.4000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Accelerated Jacobi-Gradient Iterative Algorithm to Solve the Matrix Equation \\\\({\\\\varvec{A}}\\\\boldsymbol{ Z}-\\\\overline{\\\\boldsymbol{ Z}}{\\\\varvec{B}}={\\\\varvec{C}}\\\\)\",\"authors\":\"Ahmed M. E. Bayoumi\",\"doi\":\"10.1007/s40995-024-01629-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we present an accelerated Jacobi-gradient-based iterative AJGI algorithm to solve the matrix equation <span>\\\\(A{ Z}-\\\\overline{ Z}B=C\\\\)</span>, which is based on algorithms presented by Bayoumi (Appl Math Inf Sci, 2021). The iterative solution converges to the exact solution for any initial value under appropriate assumptions. Numerical examples are provided to support the suggested approach and verify its effectiveness and accuracy when compared to a recent one previously described in Bayoumi (Appl Math Inf Sci, 2021).</p></div>\",\"PeriodicalId\":600,\"journal\":{\"name\":\"Iranian Journal of Science and Technology, Transactions A: Science\",\"volume\":\"48 3\",\"pages\":\"659 - 666\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iranian Journal of Science and Technology, Transactions A: Science\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40995-024-01629-5\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-024-01629-5","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们提出了一种基于雅各比梯度的加速迭代 AJGI 算法来求解矩阵方程 \(A{ Z}-\overline{ Z}B=C\) ，该算法基于 Bayoumi 提出的算法（Appl Math Inf Sci, 2021）。在适当的假设条件下，对于任何初始值，迭代解都能收敛到精确解。我们提供了数值示例来支持所建议的方法，并与 Bayoumi（Appl Math Inf Sci, 2021）之前描述的最新方法相比，验证了其有效性和准确性。
An Accelerated Jacobi-Gradient Iterative Algorithm to Solve the Matrix Equation \({\varvec{A}}\boldsymbol{ Z}-\overline{\boldsymbol{ Z}}{\varvec{B}}={\varvec{C}}\)
In this paper, we present an accelerated Jacobi-gradient-based iterative AJGI algorithm to solve the matrix equation \(A{ Z}-\overline{ Z}B=C\), which is based on algorithms presented by Bayoumi (Appl Math Inf Sci, 2021). The iterative solution converges to the exact solution for any initial value under appropriate assumptions. Numerical examples are provided to support the suggested approach and verify its effectiveness and accuracy when compared to a recent one previously described in Bayoumi (Appl Math Inf Sci, 2021).
期刊介绍：
The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences
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