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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.

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Metadaten
Author:Peter Benner, Daniel Kressner
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
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