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An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F
Joint Authors
Yin, Feng
Chen, Deqin
Huang, Guang-Xin
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-15
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
An iterative algorithm is constructed to solve the linear matrix equation pair AXB=E, CXD=F over generalized reflexive matrix X.
When the matrix equation pair AXB=E, CXD=F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors.
The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen.
Furthermore, the optimal approximate solution of AXB=E, CXD=F for a given generalized reflexive matrix X0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair AX̃B=Ẽ, CX̃D=F̃ with Ẽ=E-AX0B, F̃=F-CX0D.
Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
American Psychological Association (APA)
Chen, Deqin& Yin, Feng& Huang, Guang-Xin. 2012. An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-993308
Modern Language Association (MLA)
Chen, Deqin…[et al.]. An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F. Journal of Applied Mathematics No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-993308
American Medical Association (AMA)
Chen, Deqin& Yin, Feng& Huang, Guang-Xin. An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-993308
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993308