A spectral transform minimum residual filter diagonalization method for interior eigenvalues of physical systems

摘要

A spectral transform technique is introduced into the minimum residual (MINRES) filter diagonalization (FD) algorithm for the computation of eigenvalues of large Hermitian matrices. It is a low storage method, i.e., only four real vectors are required to calculate all bound states of the system. In the MINRES FD step, the finite Krylov subspace is built up by a Lanczos iteration using a spectral transform operator which is expanded in a series of Chebyshev polynomials. A guided spectral transform method is suggested to achieve high efficiency of this new algorithm. As an example, all even parity bound states of NO_2 have been calculated on the adiabatic ground state potential energy surface of NO_2 by a single propagation using a hyperbolic tangent function guided filter operator. The results show that the method is accurate and highly efficient. A statistical analysis of the spectrum is also given.