Some extremal properties of multivariate polynomial splines in the metric Lp(ℝd)

被引：0
|
作者：
Yongping Liu
Guiqiao Xu
机构：
[1] Beijing Normal University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2001年 / 44卷
关键词：
Multivariate polynomial splines; Infinite-dimensional width; Optimal subspace; Sobolev classes;
D O I：
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学科分类号：
摘要：
We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the (ℝd instead of the usual multivariate cardinal interpolation operators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asyrnptotically optimal for the Kolrnogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on (ℝd in the metric Lp((ℝd).
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页码：961 / 968
页数：7
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