Open AccessOptimal estimates of approximation errors for strongly positive linear operators on convex polytopes
Author(s) -
Osama Alabdali,
Allal Guessab
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202695a
Subject(s) - polytope , bounded function , voronoi diagram , mathematics , linear approximation , quadratic equation , domain (mathematical analysis) , regular polygon , partition (number theory) , linear operators , approximation algorithm , function (biology) , mathematical optimization , mathematical analysis , combinatorics , geometry , physics , nonlinear system , quantum mechanics , evolutionary biology , biology
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.