Solvability and sensitivity analysis of polynomial matrix equation \(X^s + A^TX^tA = Q\) (Q1008585)

The authors present a sufficient condition for the existence of a symmetric positive definite (SPD) solution of the polynomial matrix equation \(X^s + A^TX^tA = Q\) where \(s\) and \(t\) are nonnegative integers, the real matrices \(A\) and \(Q\) are \(n\times n\), \(Q\) is SPD. The authors define the condition number of the unique SPD solution and reduce its representation form. They give also perturbation analysis of the unique SPD solutions w.r.t. perturbations of the matrices \(A\) and \(Q\).