Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices

Pure PSVD approach to Sylvester-type quaternion matrix equations

“…Remark 4.3. In [9], the authors use QSVD to establish the simultaneous decomposition for 15 matrices A j , B j , C j , D j , and E j , which plays an important role in investigating the system of matrix equations A j X j B j + C j X j+1 D j = E j (j = 1, 2, 3). In this paper, we use PSVD for the quaternion matrices A i and B i to solve the system (3.11) directly.…”

A Numerical Approach To Generalized Periodic Sylvester Matrix Equation

“…In , explicit and complete parametric solutions to the forward‐time and the reverse‐time discrete periodic Sylvester matrix equations are derived without any constraints on the coefficient matrices. considers the problem of simultaneous decomposition of coupled generalized Sylvester matrix equations. And investigates the solvability conditions of mixed Sylvester equations.…”

“…And investigates the solvability conditions of mixed Sylvester equations. Both and do not give explicit iterative methods for solving the equation. , and are all focus on time‐invariant matrix equations, which are different from the objective equation considered in this paper.…”

The complete equivalence canonical form of four matrices over an arbitrary division ring

“…The singular value decomposition (SVD) is not only a basic approach in matrix theory, but also a powerful technique for solving problems in such diverse applications as signal processing, statistics, system and control theory and psychometrics (e.g., [8], [14], [28], [29], [30], [33]). To solve various problems, people have already extended the SVD method to a set of matrices instead of a single matrix (e.g., [1]- [9], [16]- [18], [20], [21], [22], [32], [34], [35], [47], [51]).…”