The Use of Lanczos's Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
Pagination or Media Count:
The generalized eigenvalue problem, Kx lambda Mx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. A new algorithm, LANZ, based on Lanczoss method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczoss method is described. A modification of Parlett and Scotts selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code.
- Theoretical Mathematics