Knot positions for the smoothest periodic quadratic spline interpolation of equispaced data Original Research Article

The knot positions of a periodic quadratic spline function which furnishes the smoothest interpolation of equispaced data are clarified. It is proved that the knots are to be at the midpoints of every two adjacent data points for the smoothest interpolation. This gives a partial answer to the problem where to locate the knots to obtain the smoothest spline interpolation of even degree.