Block-row and block-column iterative algorithms for solving linear matrix equation
Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form A x = f , motivating us to investigate the algorithm for solving the linear matrix equation A x = f . By dividing the coefficient matrix A into row blocks or colum...
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| Vydané v: | Computational & applied mathematics Ročník 42; číslo 4 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer International Publishing
01.06.2023
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| ISSN: | 2238-3603, 1807-0302 |
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| Abstract | Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form
A
x
=
f
, motivating us to investigate the algorithm for solving the linear matrix equation
A
x
=
f
. By dividing the coefficient matrix
A
into row blocks or column blocks, a block-row iterative (BRI) algorithm, a block-column iterative (BCI) algorithm and an accelerated block-column iterative (ABCI) algorithm are developed to solve
A
x
=
f
. It is successfully proved that the numerical solution produced by the proposed algorithms can converge to the exact solution for any given initial vector under appropriate conditions. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed algorithms. |
|---|---|
| AbstractList | Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form
A
x
=
f
, motivating us to investigate the algorithm for solving the linear matrix equation
A
x
=
f
. By dividing the coefficient matrix
A
into row blocks or column blocks, a block-row iterative (BRI) algorithm, a block-column iterative (BCI) algorithm and an accelerated block-column iterative (ABCI) algorithm are developed to solve
A
x
=
f
. It is successfully proved that the numerical solution produced by the proposed algorithms can converge to the exact solution for any given initial vector under appropriate conditions. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed algorithms. |
| ArticleNumber | 174 |
| Author | Liu, Duo Wang, Wenli Song, Caiqin Qu, Gangrong |
| Author_xml | – sequence: 1 givenname: Wenli surname: Wang fullname: Wang, Wenli organization: School of Mathematics and Statistics, Beijing Jiaotong University – sequence: 2 givenname: Gangrong surname: Qu fullname: Qu, Gangrong email: grqu@bjtu.edu.cn organization: School of Mathematics and Statistics, Beijing Jiaotong University – sequence: 3 givenname: Caiqin surname: Song fullname: Song, Caiqin email: songcaiqin1983@163.com organization: School of Mathematical Sciences, University of Jinan – sequence: 4 givenname: Duo surname: Liu fullname: Liu, Duo organization: School of Mathematics and Statistics, Beijing Jiaotong University |
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| Cites_doi | 10.1109/TAC.2005.852558 10.1016/j.jfranklin.2016.11.030 10.1080/00207160802123458 10.1007/s40314-021-01579-3 10.1016/j.apnum.2021.06.006 10.1186/s13662-019-2036-1 10.1016/j.jfranklin.2021.01.040 10.3182/20070829-3-RU-4912.00030 10.1007/s10915-022-02058-5 10.1016/j.jfranklin.2022.09.049 10.1016/j.sysconle.2004.06.008 10.1016/j.automatica.2004.10.010 10.1016/j.ejcon.2020.07.008 10.1016/j.cam.2021.113494 10.1007/s41980-019-00205-7 10.1007/s40314-020-01335-z 10.1016/j.jfranklin.2020.02.026 10.1007/s12190-020-01486-6 10.1016/j.jfranklin.2017.09.005 10.1137/20M133751X 10.1016/j.jfranklin.2021.05.012 10.1007/s40314-021-01523-5 10.1080/03081087.2019.1704213 10.1007/s40314-021-01628-x 10.1016/j.jfranklin.2022.05.023 10.1016/j.apm.2011.03.038 10.1109/9.489286 10.1109/9.250470 10.1007/s40314-019-0921-6 10.1016/j.jfranklin.2015.03.011 10.1016/j.camwa.2021.04.026 10.1016/j.jfranklin.2018.04.008 10.1007/s13398-020-00826-2 10.1016/j.amc.2010.05.029 10.1016/j.amc.2011.11.055 10.1016/j.amc.2015.07.022 |
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| Copyright_xml | – notice: The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Accelerated block-column iterative algorithm 15A24 65F10 15A21 Gradient-based iterative algorithm Linear matrix equation Block-row iterative algorithm Block-column iterative algorithm |
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| Snippet | Using tools like the Kronecker product and the vector operator, various Sylvester matrix equations can always be converted into the form
A
x
=
f
, motivating... |
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| Title | Block-row and block-column iterative algorithms for solving linear matrix equation |
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