Dear all,

frequently, one finds (especially in non-math publications) statements like "larger eigenvalues are computed more stably than small eigenvalues". In my understanding, such statements might be true for simple power methods. However, looking at the formulas given for the condition of eigenvalues given in the Lapack user guide, the magnitude of the eigenvalues does not enter. Moreover, modern eigenvalue methods use shifts, and hence should not suffer from this problem.

Is there in LAPACK today still any truth to "larger eigenvalues are computed more stably than small eigenvalues"?