A SHIFTED BLOCK LANCZOS-ALGORITHM FOR SOLVING SPARSE SYMMETRICAL GENERALIZED EIGENPROBLEMS

An ''industrial strength'' algorithm for solving sparse symmetric gene ralized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczo s algorithm. However, the combination of these two techniques is not t rivial; there are many pitfalls awaiting the unwary implementor. The f ocus of this paper is on identifying those pitfalls and avoiding them, leading to a ''bomb-proof'' algorithm that can live as a black box ei gensolver inside a large applications code. The code that results comp rises a robust shift selection strategy and a block Lanczos algorithm that is a novel combination of new techniques and extensions of old te chniques.