$C^1$ HERMITE INTERPOLATION WITH MPH QUARTICS USING THE SPEED REPARAMETRIZATION METHOD

In this paper, we propose a new method to obtain MPH quartic Hermite interpolants generically for any Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes ( Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find Hermite interpolants for any Hermite data generically, whether it is admissible or not.