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LSMR Iterative Method for General Coupled Matrix Equations
Joint Authors
Toutounian, F.
Khojasteh Salkuyeh, D.
Mojarrab, M.
Source
Journal of Applied Mathematics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-23
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Toutounian, F.& Khojasteh Salkuyeh, D.& Mojarrab, M.. 2015. LSMR Iterative Method for General Coupled Matrix Equations. Journal of Applied Mathematics،Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1067100
Modern Language Association (MLA)
Toutounian, F.…[et al.]. LSMR Iterative Method for General Coupled Matrix Equations. Journal of Applied Mathematics No. 2015 (2015), pp.1-12.
https://search.emarefa.net/detail/BIM-1067100
American Medical Association (AMA)
Toutounian, F.& Khojasteh Salkuyeh, D.& Mojarrab, M.. LSMR Iterative Method for General Coupled Matrix Equations. Journal of Applied Mathematics. 2015. Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1067100
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1067100