Optimal error bounds for Hermite interpolation

Error bounds for bivariate piecewise hermite interpolation

Lp-error bounds for Hermite interpolation and the associated Wirtinger inequalities

The B-spline representation for divided di erences is used, for the rst time, to provide Lp-bounds for the error in Hermite interpolation, and its derivatives, thereby simplifying and improving the results to be found in the extensive literature on the problem. These bounds are equivalent to certain Wirtinger inequalities (cf. [FMP91:p66]). The major result is the inequality jf(x) H f(x)j n 1=q...

Optimal Geometric Hermite Interpolation of Curves

Bernstein{B ezier two{point Hermite G 2 interpolants to plane and space curves can be of degree up to 5, depending on the situation. We give a complete characterization for the cases of degree 3 to 5 and prove that rational representations are only required for degree 3. x1. Introduction and Overview We consider recovery of curves from irregularly sampled data. If the curves are to be represent...

Error bounds for anisotropic RBF interpolation

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the...

Error Bounds for Polynomial Spline Interpolation

New upper and lower bounds for the L2 and Vo norms of derivatives of the error in polynomial spline interpolation are derived. These results improve corresponding results of Ahlberg, Nilson, and Walsh, cf. [1], and Schultz and Varga, cf. [5].