Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces Wr1*

Citation:

Guiqiao XU,Zehong LIU,Hui WANG.Sample Numbers and Optimal Lagrange Interpolation of Sobolev Spaces Wr1*[J].Chinese Annals of Mathematics B,2021,42(4):519~528
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Authors:

Guiqiao XU; Zehong LIU;Hui WANG

Foundation:

National Natural Science Foundation of China (Nos. 11871006,11671271).
Abstract: This paper investigates the optimal recovery of Sobolev spaces Wr1[?1, 1], r ∈ N in the space L1[?1, 1]. They obtain the values of the sampling numbers of Wr1[?1, 1] in L1[?1, 1] and show that the Lagrange interpolation algorithms based on the extreme points of Chebyshev polynomials are optimal algorithms. Meanwhile, they prove that the extreme points of Chebyshev polynomials are optimal Lagrange interpolation nodes.

Keywords:

Worst case setting, Sampling number, Optimal Lagrange interpolation nodes, Sobolev space

Classification:

41A05, 41A25
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