A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations
In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4&am...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2024-09, Vol.47 (14), p.11611-11641 |
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| creator | Long, Yanping Cui, Jingjing Huang, Zhengge Wu, Xiaowen |
| description | In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations
A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4=E $$. By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods. |
| doi_str_mv | 10.1002/mma.10146 |
| format | Article |
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A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4=E $$. By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods.]]></description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.10146</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>complex conjugate and transpose matrix equation ; Conjugates ; Convergence ; hierarchical identification principle ; Iterative algorithms ; modified gradient‐based iterative algorithm ; real representation</subject><ispartof>Mathematical methods in the applied sciences, 2024-09, Vol.47 (14), p.11611-11641</ispartof><rights>2024 John Wiley & Sons Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2576-2b4432b4ece963836e85c1f174ded501a985af829a707f7ebd7e21c7b99799323</cites><orcidid>0000-0003-2294-972X ; 0000-0002-2677-013X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.10146$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.10146$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Long, Yanping</creatorcontrib><creatorcontrib>Cui, Jingjing</creatorcontrib><creatorcontrib>Huang, Zhengge</creatorcontrib><creatorcontrib>Wu, Xiaowen</creatorcontrib><title>A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations</title><title>Mathematical methods in the applied sciences</title><description><![CDATA[In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations
A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4=E $$. By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods.]]></description><subject>complex conjugate and transpose matrix equation</subject><subject>Conjugates</subject><subject>Convergence</subject><subject>hierarchical identification principle</subject><subject>Iterative algorithms</subject><subject>modified gradient‐based iterative algorithm</subject><subject>real representation</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQhS0EEqWw4AaWWLEItZ0fx8uq4k9qxQbWlpNMUldJnNpOaXccgTNyEgxly2beaPTNe9JD6JqSO0oIm3WdCgtNshM0oUSIiCY8O0UTQjmJEkaTc3Th3IYQklPKJmiY485UutZQ4caqSkPvvz4-C-XCQXuwyusdYNU2xmq_7nBtLHam3em-wX4NuDTd0MI-aL8ZG-UD21fYW9W7wTjAnfJW7zFsx-BkeneJzmrVOrj60yl6e7h_XTxFy5fH58V8GZUs5VnEiiSJw4ASRBbncQZ5WtKa8qSCKiVUiTxVdc6E4oTXHIqKA6MlL4TgQsQsnqKbo-9gzXYE5-XGjLYPkTImIhE0jvMsULdHqrTGOQu1HKzulD1ISuRPoTIUKn8LDezsyL7rFg7_g3K1mh8_vgEN1Hm2</recordid><startdate>20240930</startdate><enddate>20240930</enddate><creator>Long, Yanping</creator><creator>Cui, Jingjing</creator><creator>Huang, Zhengge</creator><creator>Wu, Xiaowen</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0003-2294-972X</orcidid><orcidid>https://orcid.org/0000-0002-2677-013X</orcidid></search><sort><creationdate>20240930</creationdate><title>A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations</title><author>Long, Yanping ; Cui, Jingjing ; Huang, Zhengge ; Wu, Xiaowen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2576-2b4432b4ece963836e85c1f174ded501a985af829a707f7ebd7e21c7b99799323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>complex conjugate and transpose matrix equation</topic><topic>Conjugates</topic><topic>Convergence</topic><topic>hierarchical identification principle</topic><topic>Iterative algorithms</topic><topic>modified gradient‐based iterative algorithm</topic><topic>real representation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Long, Yanping</creatorcontrib><creatorcontrib>Cui, Jingjing</creatorcontrib><creatorcontrib>Huang, Zhengge</creatorcontrib><creatorcontrib>Wu, Xiaowen</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Long, Yanping</au><au>Cui, Jingjing</au><au>Huang, Zhengge</au><au>Wu, Xiaowen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2024-09-30</date><risdate>2024</risdate><volume>47</volume><issue>14</issue><spage>11611</spage><epage>11641</epage><pages>11611-11641</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract><![CDATA[In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations
A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4=E $$. By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods.]]></abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.10146</doi><tpages>31</tpages><orcidid>https://orcid.org/0000-0003-2294-972X</orcidid><orcidid>https://orcid.org/0000-0002-2677-013X</orcidid></addata></record> |
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| ispartof | Mathematical methods in the applied sciences, 2024-09, Vol.47 (14), p.11611-11641 |
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| language | eng |
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| source | Wiley-Blackwell Journals |
| subjects | complex conjugate and transpose matrix equation Conjugates Convergence hierarchical identification principle Iterative algorithms modified gradient‐based iterative algorithm real representation |
| title | A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations |
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