Algorithms 77-78. Uniform approximation of empirical functions being either monotone or having a fixed number of extrema
E. Pankowski (1980)
Applicationes Mathematicae
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Displaying similar documents to “The best uniform quadratic approximation of circular arcs with high accuracy”
Algorithms 77-78. Uniform approximation of empirical functions being either monotone or having a fixed number of extrema
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The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.
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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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