Given a Hamiltonian matrix H = JS with S symmetric and positive definite, we analyze a symplectic Lanczos algorithm to transform −H^2 in a symmetric and positive definite tridiagonal matrix of half size. By means of two effective restarted procedures, this algorithm is then used to compute few extreme eigenvalues of H. Numerical examples are also reported to compare the presented techniques.
On the computation of few eigenvalues of positive definite Hamiltonian matrices
AMODIO, Pierluigi
2006-01-01
Abstract
Given a Hamiltonian matrix H = JS with S symmetric and positive definite, we analyze a symplectic Lanczos algorithm to transform −H^2 in a symmetric and positive definite tridiagonal matrix of half size. By means of two effective restarted procedures, this algorithm is then used to compute few extreme eigenvalues of H. Numerical examples are also reported to compare the presented techniques.File in questo prodotto:
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