The Polya algorithm in sequence spaces

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• 作者：J.M. Quesada ; J. Ferná ; ndez-Ochoa ; J. Martí ; nez-Moreno and J. Bustamante
• 关键词：Best approximation ; Sequence spaces ; Strict uniform approximation ; Rate of convergence ; Polya algorithm
• 刊名：Journal of Approximation Theory
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：135
• 期：2
• 页码：245-257
• 全文大小：238 K

文摘

In this paper we consider the problem of best approximation in PF6-1&_mathId=mml1&_user=10&_cdi=6843&_rdoc=9&_handle=V-WA-A-W-AA-MsSAYVW-UUW-U-AABZBDZDBD-AABBECDCBD-CAEUAVWWW-AA-U&_acct=C000050221&_version=1&_userid=10&md5=8917372b1353854c19f6a9e44c150b37"">, 1<p∞. If h_p, 1<p<∞ denotes the best fc9bcbaa5d2"" title=""Click to view the MathML source"">ℓ_p-approximation of the element from a finite-dimensional affine subspace K of , hK, then , where is a best uniform approximation of h from K, the so-called strict uniform approximation. Our aim is to give a complete description of the rate of convergence of as p→∞ by proving that there are constants L₁,L₂>0 and 0a1 such that

for p large enough.