bibkey: deboor2005divideddifferences authors: Carl de Boor year: 2005 title: Divided Differences doi: null url: https://arxiv.org/abs/math/0502036 claim: Newton interpolation and divided differences, including the scalar mean-value theorem. strata_touched: [] license: citation-only triage: anchor

Divided Differences

Newton interpolation expands the exact interpolant in successive nodal products. For a real function with n continuous derivatives on an interval, its divided difference at n+1 distinct nodes equals f^(n)(xi)/n! for a point xi in their convex hull.

The derivative-to-monomial coefficient budget in UniformCoefficientBudget combines this classical relation with bounds on nodal products. Its endpoint application couples the same polynomial to both atomic supports. The reference supplies the classical interpolation method; it is not a source for the uniform finite-atomic Laplace minimax upper bound.

Verified locator

• URL: https://arxiv.org/abs/math/0502036
• Version: arXiv:math/0502036v1, submitted 2005-02-01 at 23:34:54 UTC.
• The abstract record identifies C. de Boor, Divided Differences, and the journal reference Surveys in Approximation Theory 1 (2005), 46–69.

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