  Higher-degree polynomial interpolations carried out on uniformly distributed
nodes are often plagued by {\it overfitting}, known as Runge's phenomenon. This
work investigates Runge's phenomenon and its suppression in various versions of
the matrix method for black hole quasinormal modes. It is shown that an
appropriate choice of boundary conditions gives rise to desirable suppression
of oscillations associated with the increasing Lebesgue constant. For the case
of discontinuous effective potentials, where the application of the above
boundary condition is not feasible, the recently proposed scheme with delimited
expansion domain also leads to satisfactory results. The onset of Runge's
phenomenon and its effective suppression are demonstrated by evaluating the
relevant waveforms. Furthermore, we argue that both scenarios are either
closely related to or practical imitations of the Chebyshev grid. The
implications of the present study are also addressed.
