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Improving certain Bernstein-type approximation processes

✍ Scribed by D. Cárdenas-Morales; F.J. Muñoz-Delgado


Book ID
104042358
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
521 KB
Volume
77
Category
Article
ISSN
0378-4754

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✦ Synopsis


This paper deals with a modification of the classical Bernstein polynomials defined on the unit simplex. It introduces a new sequence of non-polynomial linear operators which hold fixed the polynomials x 2 + αx and y 2 + βy with α, β ∈ [0, +∞). We study the convergence properties of the new approximation process and certain shape properties that are preserved. Finally, we compare it with Bernstein polynomials and show an improvement of the error of convergence in certain subsets of the simplex.


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