ERROR ESTIMATION ON PIECEWISE HERMITE INTERPOLATION

Error bounds for bivariate piecewise hermite interpolation

Construct Piecewise Hermite Interpolation Surface with Blending Methods

Three methods are proposed to construct a piecewise Hermite interpolation surface (PHIS), which is a piecewise algebraic surface interpolating a set of given points with associated normal directions. The surface is obtained by blending together some low-degree surface patches. Both the first and the second methods are completely local and give a surface with G-continuity. In the third construct...

Hermite interpolation by piecewise polynomial surfaces with polynomial area element

This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space R (where they are equivalent to the PN surfaces) and in the Minkowski space R (where they provide the MOS surfaces). We show generally in real vector spaces of any dimension and any metric that the Gram determinant of a parametr...

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

Hermite Interpolation Outperforms Nyström Interpolation

Hermite interpolation is shown to be much more stable than Nyström interpolation in the context of solving classic Fredholm second kind integral equations of potential theory in two dimensions using panel-based Nyström discretization. AMS subject classification (2000): 31A10,45B05,65D05,65R20.