Epi/hypo-convergence: The slice topology and saddle points approximation.

Bagh, A.

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Bollettino dell'Unione Matematica Italiana

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We discuss the performances of greedy algorithms for two problems of numerical approximation. The first one is the best approximation of an arbitrary function by an N-terms linear combination of simple functions adaptively picked within a large dictionary. The second one is the approximation of an arbitrary function by a piecewise polynomial function on an optimally adapted triangulation of cardinality N. Performance is measured in terms of convergence rate with respect to the number...

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2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10. The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes. Partially supported by grant No. 103/2007...