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Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples.

Abstract:
It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. © 2011 Society for Industrial and Applied Mathematics.
Publication status:
Published

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Publisher copy:
10.1137/090774707

Authors


Platte, RB More by this author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Kuijlaars, ABJ More by this author
Journal:
SIAM Review
Volume:
53
Issue:
2
Pages:
308-318
Publication date:
2011
DOI:
EISSN:
1095-7200
ISSN:
0036-1445
URN:
uuid:7cb1f886-b774-4a5a-88dd-c1e17ae8c885
Source identifiers:
188461
Local pid:
pubs:188461

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