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

In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = λBx, when λ is a semi-simple and finite eigenvalue, which departs from the classical analysis with the chordal norm [9]. A backward error and a condition number are derived for a choice of flexible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error associated with an eigenvalue only is also discussed. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]