Function Values Are Enough for L2-Approximation

We study the L 2 -approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number e n is the minimal worst-case error that can be achieved with n function values, whereas the approximation number a n is the minimal worst-case error...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 21; no. 4; pp. 1141 - 1151
Main Authors:	Krieg, David, Ullrich, Mario
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.08.2021 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Approximation Computer Science Economics Hilbert space Linear and Multilinear Algebras Math Applications in Computer Science Mathematical analysis Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Sampling Smoothness Sobolev space approximation Random matrices 41A46 41A25 46E35 Secondary: 41A63 60B20 Sobolev spaces with mixed smoothness Rate of convergence Sampling numbers
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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