Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations

A Numerical Approach To Generalized Periodic Sylvester Matrix Equation

“…The point considered in this paper is the generalized discrete‐time periodic Sylvester matrix equation in the form of where the known coefficient matrices and unknown solutions are periodic with T . This equation contains many forms of periodic matrix equations as its special case, such as forward periodic Sylvester matrices equations A j X j + X j + 1 B j = C j and its backward form considered in and generalized Sylvester matrix equation A X B + C X D = E investigated in . Equation plays an important role in the analysis and synthesis of periodic and time invariant systems.…”

New Finite Algorithm for Solving the Generalized Nonhomogeneous Yakubovich‐Transpose Matrix Equation

“…Iterative algorithms are one of the most successful techniques to solve linear systems and system identification [25][26][27][28][29][30]. During the last decade one can observe that by extending the iterative methods proposed for solving linear system of equations Mx = b, efficient iterative algorithms were proposed for solving several linear matrix equations [31][32][33][34][35]. For instance, a gradient based iterative algorithm was proposed for solving general linear matrix equations including the Sylvester-transpose matrix equation by extending the Jacobi iteration and by applying the hierarchical identification principle [36].…”

Least-squares symmetric and skew-symmetric solutions of the generalized Sylvester matrix equation∑i=1sAiXBi+∑Yuan1, Zuo2 2015Applied Mathematics and Computation0000View full textAdd to dashboardCite

“…For instance, by using the matrix decompositions such as the singular value decomposition (SVD), generalized singular value decomposition (GSVD), and canonical correlation decomposition of matrices (CCD), the matrix equation AXB + CY D = E have been considered by Chu [8], Xu, Wei, and Zheng [9], Shim and Chen [10] and Liao, Bai and Lei [11], etc. More recently, some efficient iterative methods, including Smith-type iterative algorithm, gradient iterative (GI) algorithm, LSQR iterative method, conjugate gradient (CG) method, generalized QMRCGSTAB algorithm and so forth, were introduced for solving various linear matrix equations [12][13][14][15][16][17][18][19][20][21][22][23][24].…”