Displaying similar documents to “Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica”

Greedy Algorithms for Adaptive Approximation

Albert Cohen (2009)

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...

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

Kyurkchiev, Nikolay, Markov, Svetoslav (2015)

Serdica Journal of Computing

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We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric....