Balancing Sparse Hamiltonian Eigenproblems
Please always quote using this URN:urn:nbn:de:0296-matheon-291
- 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 HD 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.
Author: | Peter Benner, Daniel Kressner |
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URN: | urn:nbn:de:0296-matheon-291 |
Referee: | Roswitha März |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2003/12/29 |
Release Date: | 2003/12/22 |
Preprint Number: | 18 |