An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane
Numerical Analysis
2016-04-06 v2 Complex Variables
Abstract
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error estimate for complex polynomial interpolation on a Jordan arc (or a Jordan curve) is given, which extends the well-known error estimate for polynomial interpolation on the unit interval. Moreover, this upper bound is independent of the parametrization of the curve.
Cite
@article{arxiv.1512.00924,
title = {An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane},
author = {Difeng Cai},
journal= {arXiv preprint arXiv:1512.00924},
year = {2016}
}