Iterative calculation of eigenvalues and eigenvectors of large, real matrix systems with overlap

An improved method for obtaining a few eigenvalues and eigenvectors of the symmetric matrix system is presented: where S ≠ I. The method allows us to handle larger systems more easily than any other known to the author. It requires the inversion of S, and N3 step, but thereafter each eigenvector and eigenvalue is obtained in a length of time proportional to N2. The relation of this method to the MOR and MMOR methods developed recently for handling the case, S = I, is discussed.