An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane

Difeng Cai

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arXiv · 1512.00924

An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane

Difeng Cai

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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.

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Difeng Cai. 2015-12-03. An Explicit Upper Bound for Modulus of Divided Difference on a Jordan Arc in the Complex Plane. https://arxiv.org/abs/1512.00924

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