A map of contour integral-based eigensolvers for solving generalized eigenvalue problems

Recently, contour integral-based eigensolvers 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 view point 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 on their subspace, an orthogonal condition and a problem to be applied implicitly.