Numerical determination of partial spectrum of Hermitian matrices using a Lanczos method with selective reorthogonalization

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication of eigenpairs in finite-precision arithmetic, but uses a new bound to decide when such reorthogonalization is required, and only reorthogonalizes with respect to eigenpairs within the region of interest. We investigate its performance for the Hermitian Wilson–Dirac operator (\gamma_5D) in lattice quantum chromodynamics, and compare it with previous methods.