Linear information versus function evaluations for <textbox>L2textbox>-approximation
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- 作者：Aicke Hinrichs ; Erich Novak ; Jan Vybí ; ral
- 关键词：Sampling numbers ; Approximation numbers ; Optimal rate of convergence ; Optimal recovery ; Approximation in style=""text-decoration ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WH7-4S0YXSF-1&_mathId=mml11&_user=
- 刊名：Journal of Approximation Theory
- 出版年：2008
- 出版时间：July 2008
- 年：2008
- 卷：153
- 期：1
- 页码：97-107
- 全文大小：165 K
文摘
We study algorithms for the approximation of functions, the error is measured in an style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WH7-4S0YXSF-1&_mathId=mml2&_user=1067359&_cdi=6843&_rdoc=9&_acct=C000050221&_version=1&_userid=10&md5=b55351f311fdf4441ad70c4b9285ec5d"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">L2 norm. We consider the worst case setting for a general reproducing kernel Hilbert space of functions. We analyze algorithms that use standard information consisting in n function values and we are interested in the optimal order of convergence. This is the maximal exponent b for which the worst case error of such an algorithm is of order style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WH7-4S0YXSF-1&_mathId=mml3&_user=1067359&_cdi=6843&_rdoc=9&_acct=C000050221&_version=1&_userid=10&md5=40187837e7710caa78779faa5e3acd0a"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">n-b.