Weighted splines as optimal interpolants (Q1201220)

The authors have critically examined in the paper some of the interesting properties of weighted splines considered as optimal interpolants. Interpolation is effected by means of special cubic splines which minimize a weighted semi-norm. The weight function is piecewise constant but is found on subdivision as different from the one determined by the interpolation knots. Two theorems and a proposition are given. The detailed values of the interpolating splines as well as the knot structure are also exhibited in nine figures.