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Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples

โœ Scribed by Platte, Rodrigo B.; Trefethen, Lloyd N.; Kuijlaars, Arno B. J.


Book ID
115470348
Publisher
Society for Industrial and Applied Mathematics
Year
2011
Tongue
English
Weight
243 KB
Volume
53
Category
Article
ISSN
0036-1445

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Exponentially accurate Runge-free approx
โœ John P. Boyd ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 477 KB

Approximating a function from its values f (x i ) at a set of evenly spaced points x i through (N + 1)-point polynomial interpolation often fails because of divergence near the endpoints, the "Runge Phenomenon". This report shows how to achieve an error that decreases exponentially fast with N . Nor