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Structured eigenvalue condition numbers
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0003-3369-2958
2006 (English)Conference paper (Refereed)Text
Abstract [en]

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product. Bounds and computable expressions for structured eigenvalue condition numbers are derived for these classes of matrices, which include complex symmetric, pseudo-symmetric, persymmetric, skew-symmetric, Hamiltonian, symplectic, and orthogonal matrices. In particular we show that under reasonable assumptions on the scalar product, the structured and unstructured eigenvalue condition numbers are equal for structures in Jordan algebras. For Lie algebras, the effect on the condition number of incorporating structure varies greatly with the structure. We identify Lie algebras for which structure does not affect the eigenvalue condition number.

Place, publisher, year, edition, pages
Philadelphia: Siam publications , 2006. Vol. 28, no 4, 1052-1068 p.
Series
, Siam journal on matrix analysis and applications, ISSN 0895-4798 ; 28:4
Keyword [en]
structured eigenvalue problem, condition number, Jordan algebra, Lie algebra, automorphism group, symplectic, perplectic, pseudo-orthogonal, pseudo-unitary, complex symmetric, persymmetric, perskew-symmetric, Hamiltonian, skew-Hamiltonian, structure preservation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-119425DOI: 10.1137/050628519ISI: 000243280600009OAI: oai:DiVA.org:umu-119425DiVA: diva2:920984
Conference
5th International Workshop on Accurate Solution of Eigenvalue Problems, JUN 29-JUL 01, 2004, Hagen, GERMANY
Available from: 2016-04-19 Created: 2016-04-18 Last updated: 2016-04-19Bibliographically approved

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Kressner, Daniel
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