An iterative algorithm for the generalized reflexive solution of the matrix equations \(AXB = E, CXD = F\)
Summary: An iterative algorithm is constructed to solve the linear matrix equation pair \(AXB = E, CXD = F\) over generalized reflexive matrix \(X\). When the matrix equation pair \(AXB = E, CXD = F\) is consistent over generalized reflexive matrix \(X\), for any generalized reflexive initial iterative matrix \(X_1\), the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of \(AXB = E, CXD = F\) for a given generalized reflexive matrix \(X_0\) can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair \(A\tilde{X}B = \tilde{E}, C\tilde{X}D = \tilde{F}\) with \(\tilde{E} = E - AX_0B, \tilde{F} = F - CX_0D\). Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
scientific article; zbMATH DE number 6106226
scientific article