Original article: Saturation in multivariate simultaneous approximation

Authors:
D. Cárdenas-Morales;A. Fraguela;P. Garrancho
Affiliations:
Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spain;Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 sur San Manuel CU., 72570 Puebla, Pue., Mexico;Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spain
Venue:
Mathematics and Computers in Simulation
Year:
2011

Citing 2
Cited 0

Asymptotic formulae of multivariate Bernstein approximation

Journal of Approximation Theory
Asymptotic expansion of multivariate conservative linear operators

Journal of Computational and Applied Mathematics

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Abstract

In this paper we present a new result on the saturation of sequences of linear operators in a multivariate and simultaneous setting. Specifically, a small o saturation result is obtained for the partial derivatives of the classical Bernstein bivariate operators on the unit simplex. Solutions of boundary value problems for certain partial differential equations of elliptic type play an important role.