ASYMPTOTIC PERTURBATION OF PALINDROMIC EIGENVALUE PROBLEMS

Abstract

We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic $P(\lambda) \equiv \lambda^2 A_1^T + \lambda A_0 + A_1$, with $A_0,\, A_1 \in \mathbb{C}^{n \times n}$ and $A_0^T = A_0$. The perturbation of eigenvalues and eigenvectors, in terms of palindromic matrix polynomials and palindromic linearizations, are discussed using Sun's implicit function approach.