Approximation by ridge function fields over compact sets

Authors:
Bruno Pelletier
Affiliations:
Laboratoire de Mathématiques Appliquées, Université du Havre, 25 rue Philippe Lebon, 76063 Le Havre, France
Venue:
Journal of Approximation Theory
Year:
2004

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Abstract

We study the approximation of a continuous function feld over a compact set T by a continuous field of ridge approximants over T, named ridge function fields. We first give general density results about function fields and show how they apply to ridge function fields. We next discuss the parameterization of sets of ridge function fields and give additional density results for a class of continuous ridge function fields that admits a weak parameterization. Finally, we discuss the construction of the elements in that class.