Generalized Taylor's Theorem

Garret Sobczyk

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arXiv · 0710.0143

Generalized Taylor's Theorem

Garret Sobczyk

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Abstract

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given multiplicities. Taken together with a simple expression for the remainder, this theorem becomes a powerful tool for approximation and interpolation in numerical analysis. We also have a corresponding theorem for rational approximation.

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Garret Sobczyk. 2007-09-30. Generalized Taylor's Theorem. https://arxiv.org/abs/0710.0143

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