Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations

2014 ◽  
Vol 34 (2) ◽  
pp. 755-771 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Discrete Time ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations

Finding solutions for periodic discrete-time generalized coupled Sylvester matrix equations via the generalized BCR method

2016 ◽  
Vol 40 (2) ◽  
pp. 647-656 ◽  
Author(s):  
Masoud Hajarian
Keyword(s):  
Iterative Method ◽  
Finite Number ◽  
Discrete Time ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Bcr Method ◽  
Residual Algorithm ◽  
Sylvester Matrix Equations ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

The periodic discrete-time matrix equations have wide applications in stability theory, control theory and perturbation analysis. In this work, the biconjugate residual algorithm is generalized to construct a matrix iterative method to solve the periodic discrete-time generalized coupled Sylvester matrix equations [Formula: see text] The constructed method is shown to be convergent in a finite number of iterations in the absence of round-off errors. By comparing with other similar methods in practical computation, we give numerical results to demonstrate the accuracy and the numerical superiority of the constructed method.

Parameterized solution to a class of sylvester matrix equations

2010 ◽  
Vol 7 (4) ◽  
pp. 479-483
Author(s):  
Yu-Peng Qiao ◽  
Hong-Sheng Qi ◽  
Dai-Zhan Cheng
Keyword(s):  
Matrix Equations ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations

scholarly journals Network Flows that Solve Sylvester Matrix Equations

2021 ◽  
pp. 1-1
Author(s):  
Wen Deng ◽  
Yiguang Hong ◽  
Brian D.O. Anderson ◽  
Guodong Shi
Keyword(s):  
Network Flows ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations

scholarly journals An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Feng Yin ◽  
Guang-Xin Huang
Keyword(s):  
Iterative Algorithm ◽  
Special Kind ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Special Cases ◽  
The Matrix ◽  
Solution Pair ◽  
Sylvester Matrix Equations ◽  
Matrix Pair

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations(AXB-CYD,EXF-GYH)=(M,N), which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matricesXandY. When the matrix equations are consistent, for any initial generalized reflexive matrix pair[X1,Y1], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair[X̂,Ŷ]to a given matrix pair[X0,Y0]in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair[X̃*,Ỹ*]of a new corresponding generalized coupled Sylvester matrix equation pair(AX̃B-CỸD,EX̃F-GỸH)=(M̃,Ñ), whereM̃=M-AX0B+CY0D,Ñ=N-EX0F+GY0H. Several numerical examples are given to show the effectiveness of the presented iterative algorithm.

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