Rate of convergence of the discrete Pólya Algorithm

Egger, A.; Huotari, Robert

doi:10.1016/0021-9045(90)90070-7

Cited by 17 publications

(12 citation statements)

References 8 publications

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“…In the literature the convergence (2) is called the Pólya Algorithm [9]. In [3,8] it is proved that if K is an affine subspace then a stronger result holds, namely that lim sup…”

Section: This Condition Can Be Writtenmentioning

confidence: 99%

Rate of convergence of the Pólya algorithm from polyhedral sets

Huotari

Marano

Navas

et al. 2005

Journal of Approximation Theory

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In this paper we consider a problem of best approximation in p , 1 < p ∞. Let h p denote the best p-approximation of h ∈ R n from a closed, convex set K of R n , 1 < p < ∞, h / ∈ K, and let h * ∞ be the strict uniform approximation of h from K. We prove that if K satisfies locally a geometrical property, fulfilled by any polyhedral set of R n , then lim sup p→∞ p h p − h * ∞ < ∞.

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“…In the literature the convergence (2) is called the Pólya Algorithm [9]. In [3,8] it is proved that if K is an affine subspace then a stronger result holds, namely that lim sup…”

Section: This Condition Can Be Writtenmentioning

confidence: 99%

Rate of convergence of the Pólya algorithm from polyhedral sets

Huotari

Marano

Navas

et al. 2005

Journal of Approximation Theory

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“…In [2,4] it is proved that the convergence of h p to h* occurs at a rate no worse than 1Âp. In [4] the authors give a necessary and sufficient condition on K for h p to coincide with h* for p large, and also a necessary and sufficient condition for…”

Section: Introductionmentioning

confidence: 97%

“…The aim of this paper is to give a detailed description of the rate of convergence of the Polya algorithm; more precisely, we prove that if (2) holds then there is a number 0<a<1 such that p &h p &h* &Âa p is bounded.…”

Section: Introductionmentioning

confidence: 99%

Rate of Convergence of the Linear Discrete Polya Algorithm

Quesada

Martínez-Moreno

Navas

et al. 2001

Journal of Approximation Theory

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“…In the literature, the convergence above is called Polya algorithm and occurs at a rate no worse than 1=p; (see [2,5]). The aim of this paper is to prove that the best ' p -approximation h p has an asymptotic expansion of the form…”

mentioning

confidence: 98%

“…Then, for all r 2 N; there are a l 2 R n ; 14l4r; such that Proof. Since p jjh p À h n 1 jj is bounded [2,5], the proof follows immediately by induction on r with the help of Lemmas 3.1 and 3.2. ] Lemma 3.1.…”

mentioning

confidence: 99%