Numerical algorithm design and analysis for the solution of QEPs are still an active research topic. Besides those methods discussed in this section, some alternative methods are available in the literature; see, for example, [284,277,372,102,209]. Most of these methods are variants of Newton's method. They generally have good local convergence properties and find one eigenpair at a time. In [209], a proper deflation technique was presented for finding more than one eigenpair.
Recently, backward errors and condition of numbers for the quadratic eigenvalue problem, and more generally, the polynomial eigenvalue problem, was presented in [435]. In [432], a perturbation analysis of the quadratic eigenvalue problem (9.2) was presented.