On upper bounds for the spectral variation of two regular matrix pairs

Upper bounds for the spectral variation of two regular matrix pairs have been given in [Guoxing Wu, Optimal bounds for the spectral variation of two regular matrix pairs, Linear Algebra Appl. 418 (2006)891–899; G.W. Stewart, An Elsner-like perturbation theorem for generalized eigenvalues, Linear Algebra Appl. 390 (2004) 1–5; Ren-cang Li, On the variation of the spectra of matrix pencils, Linear Algebra Appl. 139 (1990) 147–164]. In this note we show that some of the upper bounds are optimal and some others are strict.