An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation \(AXB=C\) (Q2468129)

The authors introduce a simple algorithm to decide whether the matrix equation \(AXB=C\) with compatibly dimensioned given matrices \(A, B\), and \(C\) has a skew-symmetric solution \(X\). The algorithm finds this solution -- if possible -- in finitely many iterations for any given error bound. Moreover the same matrix equation for a modified right hand side \(\tilde C\) and \(\tilde X\) can be used to find the minimal norm skew-symmetric solution \(X\) to the original \(AXB=C\) equation. Both algorithms work for any skew-symmetric starting matrix.