arXiv:1512.00924 Abstract | arXiv Analytics

arXiv:1512.00924 [math.NA]Abstract References Reviews Resources

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

Published 2015-12-03Version 1

An explicit upper bound is derived for the modulus of divided difference for a function defined on a Jordan arc (or a 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.

Categories: math.NA

Subjects: 65D05, 65E05, 30E05, 65Q10

Keywords: explicit upper bound, jordan arc, complex plane, divided difference, jordan curve

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