Solving Nonlinear Eigenvalue Problems via Contour Integration and Region Partitioning

ABSTRACT In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral‐based, region partitioning eigensolver for nonlinear eigenvalue problems. A new partitioning criterion is employed to eliminate the need for a problem‐dependent parameter, making our algorithm much more robust compared to the original RIM. Our algorithm can be directly applied to regions containing singularities or accumulation points, which are typically challenging for existing nonlinear eigensolvers to handle. Moreover, implementation details are provided to discuss the potential gains of combining Krylov algorithms such as infGMRES and CORK in our algorithm. Comprehensive numerical experiments are provided to demonstrate that the proposed algorithm is particularly well‐suited for dealing with regions including many eigenvalues.