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Article Dans Une Revue Analysis in Theory and Applications Année : 2006

Generalization of the interaction between the Haar approximation and polynomial operators to higher order methods

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François Chaplais

Résumé

In applications it is useful to compute the local average of a function f(u) of an input u from empirical statistics on u. A very simple relation exists when the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.
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Dates et versions

hal-00492442 , version 1 (15-06-2010)

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François Chaplais. Generalization of the interaction between the Haar approximation and polynomial operators to higher order methods. Analysis in Theory and Applications, 2006, pp.301-318. ⟨10.1007/s10496-006-0301-0⟩. ⟨hal-00492442⟩
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