Structured least-squares problems and inverse eigenvalue problems for (P,Q)(P,Q)-reflexive matrices

A new meaningful structured matrix—(P,Q)(P,Q)-reflexive matrix is defined. Without the common assumption that P or Q is unitary, a general solution is derived for its structured least-squares problem. As a necessary and sufficient condition being presented for the solvability of its structured inverse eigenvalue problem, structured constrains are firstly given to guarantee the existence of the solution. The optimal approximation problem is also considered under spectral constrains.