LSMR Iterative Method for General Coupled Matrix Equations.
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| Title: | LSMR Iterative Method for General Coupled Matrix Equations. |
|---|---|
| Authors: | Toutounian, F.1,2 toutouni@math.um.ac.ir, Khojasteh Salkuyeh, D.3 khojasteh@guilan.ac.ir, Mojarrab, M.1 maryam.modjarrab@gmail.com |
| Source: | Journal of Applied Mathematics. 3/23/2015, Vol. 2015, p1-12. 12p. |
| Subjects: | Sylvester matrix equations, Matrix groups, Frobenius algebras, Associative algebras, Numerical analysis |
| Abstract: | By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and (R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group (X1(0),X2(0),…,Xq(0)), a solution group (X1*,X2*,…,Xq*) can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group (X¯1,X¯2,…,X¯q) in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: LSMR Iterative Method for General Coupled Matrix Equations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Toutounian%2C+F%2E%22">Toutounian, F.</searchLink><relatesTo>1,2</relatesTo><i> toutouni@math.um.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Khojasteh+Salkuyeh%2C+D%2E%22">Khojasteh Salkuyeh, D.</searchLink><relatesTo>3</relatesTo><i> khojasteh@guilan.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Mojarrab%2C+M%2E%22">Mojarrab, M.</searchLink><relatesTo>1</relatesTo><i> maryam.modjarrab@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 3/23/2015, Vol. 2015, p1-12. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Sylvester+matrix+equations%22">Sylvester matrix equations</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+groups%22">Matrix groups</searchLink><br /><searchLink fieldCode="DE" term="%22Frobenius+algebras%22">Frobenius algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Associative+algebras%22">Associative algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and (R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group (X1(0),X2(0),…,Xq(0)), a solution group (X1*,X2*,…,Xq*) can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group (X¯1,X¯2,…,X¯q) in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/2015/562529 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1 Subjects: – SubjectFull: Sylvester matrix equations Type: general – SubjectFull: Matrix groups Type: general – SubjectFull: Frobenius algebras Type: general – SubjectFull: Associative algebras Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: LSMR Iterative Method for General Coupled Matrix Equations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Toutounian, F. – PersonEntity: Name: NameFull: Khojasteh Salkuyeh, D. – PersonEntity: Name: NameFull: Mojarrab, M. IsPartOfRelationships: – BibEntity: Dates: – D: 23 M: 03 Text: 3/23/2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2015 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
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