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

作者：Johnson Chris^*; Kennedy A D

来源：Computer Physics Communications, 2013, 184(3): 689-697.

DOI：10.1016/j.cpc.2012.11.003

• Spectrum
• Lanczos
• Krylov
• Eigenvalue
• Eigenvector
• Hermitian
• LANSO
• Lattice

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 D-5 in lattice quantum chromodynamics, and compare it with previous methods.

• 出版日期2013-3