Simultaneous Approximation of a Multivariate Function and its Derivatives by Multilinear Splines

2013/08/24 by Ryan Anderson, Anderson, Ryan, Yuliya Babenko +3
Mathematics · #41A05 #41A10 #41A28 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1308.5267

openalex publication_date 2013/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation error on classes of functions with moduli of continuity bounded above by certain majorants.

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