Numerical linear algebra has several important applications in a wide variety of scientific and engineering applications. The generalized eigenvalue problem, Kx= lamda Mx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problem. New software, LANZ, based on Lanczos' method is being developed for solving these problems. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. Improved method for solving symmetric indefinite linear systems and for finding eigenvalues of the tridiagonal matrices that arise when using Lanczos' method are being studied. A modification of Parlett and Scott's selective orthogonalization algorithm is being tested. Implementations of LANZ on a Convex C-220, Cray 2 and Cray Y-MP are being used to study the performance of the improved method and compare it with a subspace iteration code used by structural engineers. Research leading to an efficient, robust implementation of LANZ on MIMD parallel systems with a large number of processors is proposed.
