Abstract: In order to reasonably determine the free parameter of the cubic Cardinal spline function, the optimization of the free parameter of the cubic Cardinal spline function in the interpolation problems are discussed. Firstly, the influence of the free parameter on the curve shape of the cubic Cardinal spline function is analyzed. Secondly, the schemes for computing the optimal free parameter in the two cases of data interpolation and function approximation are given, and the cubic Cardinal spline function with mi nimal quadratic average oscillation and approximation error are obtained respectively. When it is necessary to construct the cubic Cardinal spline function with good shape preserving effect or approximation effect, the optimal free parameter can be selected by the proposed schemes.

Key words: cubic Cardinal spline function, free parameter selection, minimal quadratic average oscillation, minimal approximation error