Iterative eigenvalue method using the Bloch wave operator formalism with Padé approximants and absorbing boundaries.
We present an iterative method for calculating eigenvalues and eigenvectors of large non-Hermitian matrices. The method uses an iterative procedure to solve the basic Bloch equation HOmega=OmegaHOmega of wave operator theory. It involves nonlinear transformations such as the translation of diagonal matrix elements in the complex plane and the use of Padé approximants to treat the strongly coupled states which constitute an intermediate space around the model space. In the particular case of Floquet eigenstates the further step of adding time-dependent absorbing boundaries significantly improves the convergence properties of the iterative calculations.
Jolicard
Georges
G
Laboratoire d'Astrophysique de l'Observatoire de Besançon (CNRS UMR 6091), 41 bis Avenue de l'Observatoire, Boîte Postale 1615, 25010 Besançon Cedex, France.
Viennot
David
D
Killingbeck
John P
JP
Zucconi
Jean-Marc
JM