Contour Integral Eigensolver for Non-Hermitian Systems: A Rayleigh-Ritz-Type Approach

The Rayleigh-Ritz-type approach of the contour integral (CIRR) eigensolver is extended to be generally applicable to non-Hermitian systems. The CIRR method can extract only the eigenvalues in a given domain, which was previously formulated for non-degenerated Hermitian systems. In this method, the Ritz space for the domain is constructed by numerical evaluation of a contour integral. The effect of the numerical approximation is analyzed from the viewpoint of a filter operator, which supports the use of moderate approximations. The numerical accuracy of the original moment-based approach is also assured. A block version of the CIRR method is proposed with a detailed algorithm, which allows us to resolve degenerated systems.