Application of the Cauchy-Buniakovski-Schwarz's inequality to an optimal property for cubic splines
It is introduced the notions of oscillation of interpolation type and quadratic oscillation in average for a piecewise interpolation function. Afterwards, is obtained the cubic spline function of interpolation generated by initial conditions which have minimal quadratic oscillation in average, using the least squares method and Cauchy-Buniakowski-Schwarz's inequality.
cauchy-buniakovski-schwarz's inequality splines oscillation of interpolation type quadratic oscillation in average cubic splines generated by initial conditions