On best-approximation polynomials in the Hausdorff metric

1997 ◽  
Vol 85 (2) ◽  
pp. 1839-1848
Author(s):  
A. P. Petukhov
Keyword(s):  
Best Approximation ◽  
Hausdorff Metric

scholarly journals Polytopal approximation of elongated convex bodies

2018 ◽  
Vol 18 (1) ◽  
pp. 105-114
Author(s):  
Gilles Bonnet
Keyword(s):  
Convex Body ◽  
Best Approximation ◽  
Convex Set ◽  
Hausdorff Metric ◽  
Convex Bodies ◽  
The Best Approximation ◽  
Polytopal Approximation ◽  
Isoperimetric Ratio

AbstractThis paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex bodyKby a circumscribed polytopePwith a given number of facets. These bounds are of particular interest ifKis elongated. To measure the elongation of the convex set, its isoperimetric ratioVj(K)1/jVi(K)−1/iis used.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

Hausdorff GAN: Improving GAN Generation Quality With Hausdorff Metric

2021 ◽  
pp. 1-13 ◽  
Author(s):  
Wei Li ◽  
Zhixuan Liang ◽  
Ping Ma ◽  
Ruobei Wang ◽  
Xiaohui Cui ◽  
...  
Keyword(s):  
Hausdorff Metric
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