Structured eigenvalue condition numbers
2006 (English)Conference paper (Refereed)Text
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.
, Siam journal on matrix analysis and applications, ISSN 0895-4798 ; 28:4
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
IdentifiersURN: urn:nbn:se:umu:diva-119425DOI: 10.1137/050628519ISI: 000243280600009OAI: oai:DiVA.org:umu-119425DiVA: diva2:920984
5th International Workshop on Accurate Solution of Eigenvalue Problems, JUN 29-JUL 01, 2004, Hagen, GERMANY