Optimizing Rayleigh quotient with symmetric constraints and their applications to perturbations of the structured polynomial eigenvalue problem

Anshul Prajapati, Punit Sharma

For a Hermitian matrix $H\in {\mathbb{C}}^{n,n}$ and symmetric matrices $S_0,S_1,\dots ,S_k\in {\mathbb{C}}^{n,n}$, we consider the problem of computing the supremum of $\left\{ \frac…