A new method for smoothing surfaces and computing hermite interpolants

Let Ω be a rectangular bounded domain of a plane equipped with a rectangular partition Δ. Assume a piecewise bivariate function that is differentiable up to order (k,l) except at the knots of Δ, where it is less differentiable. In this paper, we introduce a new method for smoothing the above function at the knots. More precisely, we describe algorithms allowing one to transform it into another function that will be differentiable up to order (k,l) in the whole domain Ω. Then, as an application of this method, we give a recursive computation of tensor product Hermite spline interpolants. To illustrate our results, some numerical examples are presented.