The general coupled matrix equations over generalized bisymmetric matrices

Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations Over Generalized Reflexive Matrices

“…The applications of linear matrix equations have motivated both mathematicians and engineers to construct methods catering to solve linear matrix equations [1,4,6,7,8,9,19,23,25]. Based on Smith iterations [24], iterative methods were developed for periodic standard Lyapunov matrix equations and projected generalized Lyapunov matrix equations [27,28].…”

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].…”

Positive definite solutions of the nonlinear matrix equation X+AHX¯-1Zhou1, Cai2, Lam3 2013Applied Mathematics and Computation320190View full textAdd to dashboardCite

“…Various kinds of matrix equations have received much attention in the literature (see, for example, [4], [7], [8], [11], [12], [13], [15], [14], [16], [19], [27], [28], [29], [34], [38], [39], [40], and the references therein). Especially, the problem of finding fixed points of the nonlinear matrix equation X + A * X −1 A = Q where A and Q > 0 are given and X is unknown, has been extensively studied in the last two decades.…”