Cubic Hermite interpolation with minimal derivative oscillation

In this paper, a new optimal cubic Hermite interpolation method is presented. The method is to optimize the derivative of the interpolant. The diagonally dominant property of the obtained system of normal equations and the error bound are better than some of the existing cubic interpolants. For parametric curve design, the vector-valued interpolation method is given. Some numerical examples are provided to illustrate the satisfactory shape of the interpolation curves.