Lower bounds for the approximation with variation-diminishing splines

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• 作者：J. Naglerp>ap>p> ; p>p>johannes.nagler@uni-passau.de" class="auth_mail" title="E-mail the corresponding authorp> ; P. Cerejeirasp>bp>p> ; p>p>pceres@ua.pt" class="auth_mail" title="E-mail the corresponding authorp> ; B. Forsterp>ap>p> ; p>p>brigitte.forster@uni-passau.de" class="auth_mail" title="E-mail the corresponding authorp>
• 关键词：Schoenberg operator ; Inverse theorem ; Iterates ; Spectral theory
• 刊名：Journal of Complexity
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：32
• 期：1
• 页码：81-91
• 全文大小：373 K

文摘

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0885064X15000813&_mathId=si1.gif&_user=111111111&_pii=S0885064X15000813&_rdoc=1&_issn=0885064X&md5=179ecf511fd06a3767d0870b242ab09c" title="Click to view the MathML source">[0,1]pan>pan class="mathContainer hidden">pan class="mathCode">$[0,1]$pan>pan>pan> in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.