An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem \(AX=B\) with a submatrix constraint (Q469121)

The paper considers the problem of finding a matrix \(A\) such that \(AX=B\) and a submatrix \(A\left[ p,q\right] \) has a given value. A conjugate gradient-like algorithm is proposed, which converges in finitely many steps to a solution if the problem is consistent. A special initial value of the iterations can be found, which results in a solution that is at the minimal Frobenius distance from a given matrix. The method is illustrated by a numerical example.