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  Volume 3, Issue 4, Article 50
Rate of Convergence of the Discrete Polya Algorithm from Convex Sets. A Particular Case

    Authors: M. Marano, J. Navas, J.M. Quesada,  
    Keywords: Best uniform approximation, Rate of convergence, Polya Algorithm, Strong uniqueness.  
    Date Received: 04/12/01  
    Date Accepted: 28/05/02  
    Subject Codes:


    Editors: Alexander G. Babenko,  

In this work we deal with best approximation in $ ell_{p}^n$, $ 1<p leq infty$, $ ngeq 2$. For $ 1<p<infty$, let $ h_{p}$ denote the best $ ell_{p}^n$-approximation to $ fin mathbb{R}^n$ from a closed, convex subset $ K$ of $ mathbb{R}^n$, $ f not in K$, and let $ h^*$ be a best uniform approximation to $ f$ from $ K$. In case that $ h^*-f$ $ =(rho_1,rho_2,cdots,rho_n)$, $ vertrho_jvert=rho;$ for $ j=1,2,cdots,n$, we show that the behavior of $ Vert h_{p}-h^*Vert$ as $ p to infty$ depends on a property of separation of the set $ K$ from the $ ell^n_{infty}$-ball $ {xinmathbb{R}^n:Vert x-fVertleqrho}$ at $ h^*-f$.

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