Iterative solutions to coupled Sylvester-transpose matrix equations

Biconjugate residual algorithm for solving general Sylvester-transpose matrix equations

“…In [2], Dopico et al introduced several projection algorithms based on different Krylov spaces to find the low-rank approximations to the solution of the Sylvester-transpose matrix equation. The development of iterative methods proposed for Ax = b has gained interest to compute numerical solutions of linear matrix equations in recent years [12,21,33,[45][46][47]. By developing the conjugate gradient normal equation residual (CGNR), the conjugate gradient normal equation error (CGNE) and the least-squares QR-factorization (LSQR) algorithms, various efficient methods were constructed for solving diverse linear matrix equations [12,23,24,30].…”

Polynomial Solutions to the Matrix EquationX−AXTB=C

“…And the least squares solutions and least square solutions with the minimal-norm have been obtained. In [16], using the hierarchical identification principle, authors consider the following more general coupled Sylvester-transpose matrix equation:…”

Parametric Solutions to the Generalized Discrete Yakubovich‐Transpose Matrix Equation

“…By using the Moore‐Penrose generalized inverse, Piao et al discussed some necessary and sufficient conditions for the matrix equation AX + X T B = C . The authors in introduced an iterative algorithm for solving the matrix equation AXB + CX T D = E , generalized Sylvester‐transpose matrix equation and coupled Sylvester‐transpose matrix equation. In addition, parameter estimation is the eternal theme of system identification and many identification methods have been used for decades , e.g.…”

“…In [20], Wang considered the matrix equation AXB + CYD = E over an arbitrary regular ring with identity, and derived the necessary and sufficient conditions for the solution existence, and the expression of the general solution to the systems. By using the generalized singular value decomposition (GSVD) of matrices, Liao et al [21] studied the least squares solutions with the minimum norm for the matrix equation A T XB + B T X T A = D. By using the Moore-Penrose generalized inverse, Piao et al [22] discussed some necessary and sufficient conditions for the matrix equation AX + X T B = C. The authors in [23][24][25][26][27] introduced an iterative algorithm for solving the matrix equation AXB + CX T D = E, generalized Sylvester-transpose matrix equation and coupled Sylvester-transpose matrix equation. In addition, parameter estimation is the eternal theme of system identification and many identification methods have been used for decades [30][31][32][33], e.g.…”