β Scribed by Sergio Amat; Sonia Busquier; Antonio Escudero; J. Carlos Trillo
No coin nor oath required. For personal study only.
This note is devoted to Lagrange interpolation for continuous piecewise smooth functions. A new family of interpolatory functions with explicit approximation error bounds is obtained. We apply the theory to the classical Lagrange interpolation.
π SIMILAR VOLUMES
The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
Straight-line and circular-arc segments with weight functions are used for interpolation. The smoothness of the curve depends on the weight functions. Variable smoothness can be achieved by changing the weights. The proposed technique is useful in robotics and numerically controlled machining, becau