期刊
MATHEMATICS OF COMPUTATION
卷 76, 期 260, 页码 1981-1993出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-07-01988-6
关键词
geometric interpolation; approximation order; asymptotic analysis
In this paper the problem of geometric interpolation of planar data by parametric polynomial curves is revisited. The conjecture that a parametric polynomial curve of degree <= n can interpolate 2n given points in R-2 is confirmed for n <= 5 under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order 2n can be achieved as soon as the interpolating curve exists.
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