Disguised and new quasi-Newton methods for nonlinear eigenvalue problems (Q2413504)

Four iterative methods are explored and a way of their analyzation with techniques of quasi-Newton methods and Keldysh's theorem is given. It is shown how two well-established methods can be interpreted as quasi-Newton methods. Methods of this type can in an insightful way be analyzed in the framework of quasi-Newton methods. Linear as well as higher order convergence can be expressed in this framework. There are many results for quasi-Newton methods which can potentially be applied to these methods, e.g., techniques which improve the convergence basin, scaling techniques, adaption for non-smooth (or almost non-smooth) problems, and general convergence results.