Structured condition numbers for invariant subspaces
Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number c(S), for invariant subspaces subject to structured perturbations. Several examples compare c(S) with the unstructured condition number. The examples include block cyclic, Hamiltonian, and orthogonal matrices. This approach extends naturally to structured generalized eigenvalue problems such as palindromic matrix pencils.
Keywords: structured eigenvalue problem ; invariant subspace ; perturbation theory ; condition number ; deflating subspace ; block cyclic ; Hamiltonian ; orthogonal ; palindromic ; Computing Stable Eigendecompositions ; Perturbation Analysis ; Eigenvalue Problems ; Sylvester Equation ; Backward Error ; Algorithms ; Matrices ; Bounds ; Software ; Pencils
Record created on 2011-05-05, modified on 2016-08-09