Extremal spline bases

Abstract

AbstractIn the space of all polynomial splines on an infinite equidistant grid with fixed odd degree and with fixed period, the Lagrangians belonging to the grid-points as nodes form an extremal basis with respect to the supremum-norm. This means that no element of the basis can be approximated within the span of the other elements better than by zero. The result is carried over to the nonperiodic cardinal-spline case. Moreover, an intrinsic insight into the behaviour of the Lagrangian splines is obtained