The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem
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 Lanczos's 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 Lanczos's method is described. A modification of Parlett and Scott's 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. (KR).
"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 Lanczos's 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 Lanczos's method is described. A modification of Parlett and Scott's 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. (KR)."@en
Institute for Computer Applications in Science and Engineering.
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