期刊
SIAM REVIEW
卷 53, 期 2, 页码 308-318出版社
SIAM PUBLICATIONS
DOI: 10.1137/090774707
关键词
Runge phenomenon; Gibbs phenomenon; interpolation; radial basis functions; Lanczos iteration
资金
- UK EPSRC [EP/E045847/1]
- FWO-Flanders [G.0427.09]
- K.U. Leuven research grant [OT/08/33]
- Belgian Interuniversity [P06/02]
- Spanish Ministry of Science and Innovation [MTM2008-06689-C02-01]
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.
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