THE COMBINATION OF COMPLEX SCALING AND THE LANCZOS-ALGORITHM

We present a symbiosis of three very powerful mathematical tools: the discrete variable representation (DVR), complex scaling, and the Lanczos algorithm, by which we demonstrate that the widespread negative view on combining the Lanczos algorithm with the complex coordinate method for large systems may be too pessimistic. We apply a complex version of the DVR method suitable for homogeneous operators in the DVR, such as x, and make use of a Mobius transform inducing a spectral shift, which enhances significantly the efficiency of the complex symmetric matrix adapted Lanczos algorithm. This is done without any loss of the advantages provided by each method on its own. A numerical application to a collinear A-B-A molecule is given.