  Recently, contour integral-based methods have been actively studied for
solving interior eigenvalue problems that find all eigenvalues located in a
certain region and their corresponding eigenvectors. In this paper, we
reconsider the algorithms of the five typical contour integral-based
eigensolvers from the viewpoint of projection methods, and then map the
relationships among these methods. From the analysis, we conclude that all
contour integral-based eigensolvers can be regarded as projection methods and
can be categorized based on their subspace used, the type of projection and the
problem to which they are applied implicitly.
