Based on Peano kernel technique, explicit error bounds (optimal For the hig
hest order derivative) are proved for the derivatives of cardinal spline in
terpolation (interpolating at the knots for odd degree splines and at the m
idpoints between two knots for even degree splines). The results are based
on a new representation of the Peano kernels and on a thorough investigatio
n of their zero distributions. The bounds are given in terms of Euler-Frobe
nius polynomials and their zeros. (C) 1999 Academic Press.