| A <em>sharp</em> pointwise error estimate is given for multivariate positive linear operators which reproduce the linear polynomials. This quantitative Korovkin--type theorem generalises a known univariate result. It is applied to a number of operators including the multivariate Bernstein operators, and the recently introduced Bernstein--Schoenberg type operators of Dahmen, Micchelli and Seidel. |
Keywords
Korovkin--type theorem, positive linear operator, Bernstein operator, variation diminishing splines, multivariate Bernstein--Schoenberg type operators, radial basis function approximation
Math Review Classification
Primary 41A10, 41A65, 41A80
; Secondary 41A05, 41A55, 46E99, 65J05
Last Updated
7 May 1997
Length
8 pages
Availability
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