ABLEpack implements an adaptive block Lanczos method which extracts eigenvalues or eigentriples. This algorithm approximately solves standard non-Hermitian eigenproblems:
A x = lambda x y' A = lambda y'It can also solve generalized non-Hermitian eigenvalue problems:
A x = lambda B x y' A = lambda y' Bby using the shift and invert spectral transformation to reduce them to the following standard eigenvalue problems:
C x = mu x z' C = mu z'where
C = inv( A - alpha B ) B mu = 1 / ( lambda - alpha ) z = ( A - alpha B)' yThe user must specify the minimum number of eigenvalues to find, neig. If shift-and-invert is used, then at least neig eigenvalues clustered around the shift alpha are found.