Interpolation and Instant Approximation

Abstract

Translate Article

Interpolation methods on Chebyshev nodes give rather good approximations resp. error bounds. We show how certain improvements can be obtained with little effort: Main principle FFE (Few Function Evaluations). The remainder estimate based on one degree of approximation will be refined by introducing several such degrees (in combination with estimates for Chebyshev coefficients). Next we investigate the question whether the interpolation polynomial can be abridged (modified to a polynomial of lower degree). An error bound is obtained by considering the original nodes and the new coefficients. On the other hand we refine the interpolation process by introducing two auxiliary nodes. Finally, we mention modifications, linear programming methods and the multivariate case.