A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices (CSIAM Transactions on Applied Mathematics, 2020)
Recently a novel family of eigensolvers, called spectral indicator methods(SIMs), was proposed. Given a region on the complex plane, SIMs first compute anindicator by the spectral projection. The indicator is used to test if the region containseigenvalue(s). Then the region containing eigenvalues(s) is subdivided and tested.The procedure is repeated until the eigenvalues are identified within a specified precision. In this paper, using Cayley transformation and Krylov subspaces, a memoryefficient multilevel eigensolver is proposed. The method uses less memory comparedwith the early versions of SIMs and is particularly suitable to compute many eigenvalues of large sparse (non-Hermitian) matrices. Several examples are presented fordemonstration.