Using the least squares method and the notion of quadratic oscillation in average form, we obtain here an interpolating cubic spline having minimal quadratic oscillation in average.

It is introduced the notions of oscillation of interpolation type and quadratic oscillation in average for a piecewise interpolation function. Af- terwards, is obtained the cubic spline function of interpolation generated by initial conditions which have minimal quadratic oscillation in aver- age, using the least squares method and Cauchy-Buniakowski-Schwarz’s inequality