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New Finite Algorithm for Solving the Generalized Nonhomogeneous Yakubovich‐Transpose Matrix Equation
Author(s) -
Hajarian Masoud
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1343
Subject(s) - transpose , mathematics , matrix norm , matrix (chemical analysis) , norm (philosophy) , iterative method , computation , algorithm , algebra over a field , mathematical analysis , pure mathematics , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , political science , law , composite material
In this paper, the development of the conjugate direction (CD) method is constructed to solve the generalized nonhomogeneous Yakubovich‐transpose matrix equation A X B + C X T D + E Y F = R . We prove that the constructed method can obtain the (least Frobenius norm) solution pair ( X , Y ) of the generalized nonhomogeneous Yakubovich‐transpose matrix equation for any (special) initial matrix pair within a finite number of iterations in the absence of round‐off errors. Finally, two numerical examples show that the constructed method is more efficient than other similar iterative methods in practical computation.