A note on the normwise perturbation theory for the regular generalized eigenproblem

Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications

“…The following lemma gives an explicit expression for η(x, λ) and η(λ). This lemma generalizes results given in [36] for the 2-norm and earlier in [5], [10] for the generalized eigenvalue problem.…”

Computation of pseudospectra

“…Our discussion has been confined to the standard matrix problem Ax -Ax, that is, pseudospectra of matrices or operators, but in many applications it may be more appropriate to consider the generalized problem Ax = XBx, that is, pseudospectra of matrix or operator pencils (van Dorsselaer 1997, Fraysse, Gueury, Nicoud and Toumazou 1996, Fraysse and Toumazou 1998, Riedel 1994.…”

Structured Backward Error and Condition of Generalized Eigenvalue Problems

“…The following theorem, which is a straightforward modification of a result of Rigal and Gaches on the normwise backward error for a linear system [26], gives an explicit expression for η( x, λ). For the case α = β, this theorem and the following lemma are given by Frayssé and Toumazou [14].…”