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:\documentclass{article}\pagestyle{empty}\begin{document}$$(A - \lambda S)c = 0$$\end{document} 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 N 3 step, but thereafter each eigenvector and eigenvalue is obtained in a length of time proportional to N 2 . The relation of this method to the MOR and MMOR methods developed recently for handling the case, S = I , is discussed.