  In this chapter we are examining several iterative methods for solving
nonlinear eigenvalue problems. These arise in variational image-processing,
graph partition and classification, nonlinear physics and more. The canonical
eigenproblem we solve is $T(u)=\lambda u$, where $T:\R^n\to \R^n$ is some
bounded nonlinear operator. Other variations of eigenvalue problems are also
discussed. We present a progression of 5 algorithms, coauthored in recent years
by the author and colleagues. Each algorithm attempts to solve a unique problem
or to improve the theoretical foundations. The algorithms can be understood as
nonlinear PDE's which converge to an eigenfunction in the continuous time
domain. This allows a unique view and understanding of the discrete iterative
process. Finally, it is shown how to evaluate numerically the results, along
with some examples and insights related to priors of nonlinear denoisers, both
classical algorithms and ones based on deep networks.
