The quadratic eigenvalue problem in electric power systems
Automation and Remote Control
Eigenvalue condition numbers: zero-structured versus traditional
Journal of Computational and Applied Mathematics
Eigenvalue patterned condition numbers: Toeplitz and Hankel cases
Journal of Computational and Applied Mathematics
Eigenvalue condition numbers: Zero-structured versus traditional
Journal of Computational and Applied Mathematics
Backward errors for eigenproblem of two kinds of structured matrices
Journal of Computational and Applied Mathematics
Structured Pseudospectra and the Condition of a Nonderogatory Eigenvalue
SIAM Journal on Matrix Analysis and Applications
Structured Pseudospectra for Small Perturbations
SIAM Journal on Matrix Analysis and Applications
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We present a chart of structured backward errors for approximate eigenpairs of singly and doubly structured eigenvalue problems. We aim to give, wherever possible, formulae that are inexpensive to compute so that they can be used routinely in practice. We identify a number of problems for which the structured backward error is within a factor $\sqrt{2}$ of the unstructured backward error. This paper collects, unifies, and extends existing work on this subject.