The error in linear interpolation at the vertices of a simplex

摘要

A formula for the error in multivariate quasi-interpolation which reproduces the linear polynomials is given. From it sharp pointwise L-infinity-bounds for the error in linear interpolation (interpolation by linear polynomials) to function values at the vertices of a simplex are obtained. The corresponding 'envelope theorem' giving the optimal recovery of functions is discussed. [References: 15]