Geodesic
Optimal estimates of approximation errors for strongly positive linear operators on convex polytopes
Filomat, Tome 36 (2022) no. 2, p. 695

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DOI

In the present investigation, we introduce and study linear operators, which underestimate every strongly convex function. We call them, for brevity, sp−linear (approximation) operators. We will provide their sharp approximation errors. We show that the latter is bounded by the error approximation of the quadratic function. We use the centroidel Voronoi tessellations as a domain partition to construct best sp−linear operators. Finally, numerical examples are presented to illustrate the proposed method
DOI : 10.2298/FIL2202695A
Classification : 65D30, 65D32, 41A63, 41A44, 41A80, 26B25, 26D15, 52A40
Keywords: Multivariate approximate integration, convex functions, error estimates, Voronoi Diagram 
Osama Alabdali; Allal Guessab. Optimal estimates of approximation errors for strongly positive linear operators on convex polytopes. Filomat, Tome 36 (2022) no. 2, p. 695 . doi: 10.2298/FIL2202695A
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     author = {Osama Alabdali and Allal Guessab},
     title = {Optimal estimates of approximation errors for strongly positive linear operators on convex polytopes},
     journal = {Filomat},
     pages = {695 },
     year = {2022},
     volume = {36},
     number = {2},
     doi = {10.2298/FIL2202695A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2202695A/}
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