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Simultaneous Interpolation and Approximation by a Class of Multivariate Positive Operators

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Abstract

The purpose of this paper is to show that the interpolation positive operators of a wide class satisfy also the approximation property. Such a situation of simultaneous interpolation and approximation may be very desirable, but is rather unusual. Our attention is focused on the convergence problem, giving the conditions under which a sequence of operators of the considered class converges to a continuous function in a convex compact set in R m (m∈N). It must be recalled that many of these operators are very interesting in applications and that suitable algorithms can be devised for parallel, multistage and iterative computation.

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Authors and Affiliations

  1. Department of Mathematics, University of Turin, via Carlo Alberto 10, 10123, Torino, Italy

    Giampietro Allasia

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  1. Giampietro Allasia
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Allasia, G. Simultaneous Interpolation and Approximation by a Class of Multivariate Positive Operators. Numerical Algorithms 34, 147–158 (2003). https://doi.org/10.1023/B:NUMA.0000005359.72118.b6

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  • DOI: https://doi.org/10.1023/B:NUMA.0000005359.72118.b6

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