This paper presents a comprehensive collection of various error estimates for linear interpolation on simplices. The survey covers many relevant aspects such as geometric facts about simplices, functions of several smoothness classes and arbitrary dimension, and different forms of derivatives. Most estimates involve constants that are best possible. Extremal functions and simplices are provided for all sharp inequalities. © 2000 Academic Press.
CITATION STYLE
Stämpfle, M. (2000). Optimal Estimates for the Linear Interpolation Error on Simplices. Journal of Approximation Theory, 103(1), 78–90. https://doi.org/10.1006/jath.1999.3421
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