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

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils

“…Note that the inequality becomes an equality for the direction , . In turn, the absolute condition number of , defined as satisfies see, e.g., [ 8 , Lemma 3.1 and Eq. (3.3)].…”

Effective condition number for numerical partial differential equations

“…(5) with rank(F) =r n be given. Then from (6) the relative errors of the solution x are bounded in (14) by the Cond eff defined in (15) and by the Cond E defined in (17). Moreover, when r = 0, these errors are bounded by the Cond EE defined in (18).…”

“…The traditional condition number Cond is used in many textbooks, such as Strang [5], Atkinson [6], Schwarz [7], Datta [8], Gill et al [9], Golub and van Loan [10], Stewart [11], Horn and Johnson [12], Sun [13], Wang et al [14] and Higham [15]. The condition number for eigenvalues is introduced in Parlett [16] and Frayssé and Toumazou [17], and there are more discussions in Gulliksson and Wedin [18] and Luding et al [19]. The Cond is applied to the numerical PDEs in Strang and Fix [20], Quarteroni and Valli [21] and Li [22].…”