Generalized Taylor's Theorem

2007/09/30 by Garret Sobczyk, Sobczyk, Garret · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.0710.0143

openalex publication_date 2007/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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