Error Bounds for Lagrange Interpolation

A Multivariate Form of Hardy's Inequality and L P -error Bounds for Multivariate Lagrange Interpolation Schemes

The following multivariate generalisation of Hardy's inequality, that for m ? n=p > 0

Error bounds for bivariate piecewise hermite interpolation

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].

Anisotropic error bounds of Lagrange interpolation with any order in two and three dimensions

In this paper, using the Newton's formula of Lagrange interpolation, we present a new proof of the anisotropic error bounds for Lagrange interpolation of any order on the triangle, rectangle, tetrahedron and cube in a unified way. It is known that the polynomial interpolations are the foundations of construction the finite elements and the interpolation error estimates play a key role in derivi...