Interpolating Operators for Multiapproximation
TL;DR: In this article, the authors investigated operators that are good for best multiapproximation and best one-sided multi-parameter multi-approximation for continuous functions.
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Abstract: Problem statement: There are no simple definitions of operators for be st multiapproximation and best one sided multiapproximation which work for any measurable function in Lp for, p>0. This study investigated operators that a re good for best multiapproximation and best one sided multiapproximation. Approach: We first introduced some direct results related to the approximation problem of continuous functions by Hermit-Fejer interpolation based on the zeros of Chebyshev polynomials of the first or second kind i n terms of the usual modulus of continuity. They were then improved to spaces Lp for p 0.
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Citations
Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
TL;DR: Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K by approximating from above the indicator function with a sequence of polynomials of increasing degree d so that the integrals of these polynoms generate a convergence sequence of upper bounds on thevolume of K.
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A new scheme for approximating the weakly efficient solution set of vector rational optimization problems
Feng Guo,Liguo Jiao +1 more
TL;DR: In this paper , a scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities is presented.
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Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets
TL;DR: In this paper, the authors show that the asymptotic rate of convergence is at least O(1/ log log log d), where d is the number of polynomials of increasing degree.
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TL;DR: In this paper, the authors present a topology review of classical Banach spaces with a focus on weak compactness in L1 and C(K) spaces, and the Dunford-Pettis property of C0, l1 and l 7.
in the Approximation
A. Arnaud
- 01 Jan 1974
TL;DR: In this paper, a general theory of optical rea-tom based on the con- cept of complex pomteikond is presented and the analysis is timited to the approximation of Gaw& The modes of rwnance of open remna-bors formed by two sphaicrl minors facing each other have been ob- taiued m previous works by fitting the wavehmts of GIllardrn beans to the mirmr surfaces.