1993
DOI: 10.1017/s1446788700032043
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Tubular sets and multivariate Polya algorithm

Abstract: Some new results concerning tubular sets are presented, with applications to the convergence of the Polya algorithm in the contexts of simultaneous approximation and approximation of multivariate functions by univariate functions. (The Polya algorithm constructs a best uniform approximation from the limit, as p ->• co, of best L p approximations.) In 1913, George Polya proposed an algorithm to calculate best uniform approximations to continuous functions by polynomials [8]. This algorithm utilizes the continuu… Show more

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“…Before giving the definition of this weaker property, we recall the notion of tubularity for subsets of R N . In the study of the l ∞ -projection on a closed convex subset of R N , Huotari and Marano were led to define the notion of total tubularity for a convex set (also called property P; see [9], [10] and [12]) as a sufficient condition for the convergence of the Polya algorithm.…”
Section: Nonlinear Averages and θ-Centersmentioning
confidence: 99%
“…Before giving the definition of this weaker property, we recall the notion of tubularity for subsets of R N . In the study of the l ∞ -projection on a closed convex subset of R N , Huotari and Marano were led to define the notion of total tubularity for a convex set (also called property P; see [9], [10] and [12]) as a sufficient condition for the convergence of the Polya algorithm.…”
Section: Nonlinear Averages and θ-Centersmentioning
confidence: 99%