Balancing sparse Hamiltonian eigenproblems

Balancing a matrix by a simple and accurate similarity transformation can improve the speed and accuracy of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H. It is first shown how to permute H to irreducible form while retaining its structure. This form can be used to decompose the Hamiltonian eigenproblem into smaller-sized problems. Next, we discuss the computation of a symplectic scaling matrix D so that the norm of D-1 H D is reduced. The considered scaling algorithm is solely based on matrix-vector products and thus particularly suitable if the elements of H are not explicitly given. The merits of balancing for eigenvalue computations are illustrated by several practically relevant examples. (c) 2004 Elsevier Inc. All rights reserved.


Published in:
Linear Algebra And Its Applications, 415, 1, 3-19
Year:
2006
Publisher:
Elsevier
ISSN:
0024-3795
Keywords:
Laboratories:




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