  Explicit pointwise error bounds for the interpolation of a smooth function by
piecewise exponential splines of order four are given. Estimates known for
cubic splines are extended to a natural class of piecewise exponential splines
which are appearing in the construction of multivariate polysplines. The error
estimates are derived in an inductive way using error estimates for the
interpolation of a smooth function by exponential splines of order two.
