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In search of the best approximant
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Gzyl +2 more
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Continuity of Best Hankel Approximation and Convergence of Near-Best Approximants
SIAM Journal on Control and Optimization, 1994Summary: Consider a bounded Hankel operator \(\Gamma\) with \(s\)-numbers \(s_ 0\geq s_ 1\geq\cdots\) and a sequence of bounded Hankel operators \(\Gamma_ n\) converging to \(\Gamma\) in the operator norm. In this paper, it is shown that for each \(k\) with \(s_{k-1}> s_ k\geq s_{k+1}\geq\cdots\), the rational symbols of the best rank-\(k\) Hankel ...
Chui, Charles K., Li, Xin
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The Best Interpolating Approximation is a Limit of Best Weighted Approximations
Canadian Mathematical Bulletin, 1982AbstractUnder appropriate conditions it is shown that the best interpolating approximation to a given function in the uniform norm is a limit of best unconstrained approximations with respect to a certain sequence of discontinuous weight functions.
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Advances in Computational Mathematics, 2002
Tree approximation is a new form of nonlinear wavelet approximation. The distinction between tree approximation and the familiar \(n\)-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure.
Baraniuk, R. G. +7 more
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Tree approximation is a new form of nonlinear wavelet approximation. The distinction between tree approximation and the familiar \(n\)-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure.
Baraniuk, R. G. +7 more
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Ukrainian Mathematical Journal, 2000
Summary: We investigate a property of a sequence of polynomials of best approximation in the mean related to the convergence in a neighborhood of every point of regularity of a function on the level line \(\partial G_R\).
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Summary: We investigate a property of a sequence of polynomials of best approximation in the mean related to the convergence in a neighborhood of every point of regularity of a function on the level line \(\partial G_R\).
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EMBEDDING THEOREMS AND BEST APPROXIMATIONS
Mathematics of the USSR-Sbornik, 1975We establish necessary and sufficient conditions, in terms of best approximations, for a function in () to belong to (p$ SRC=http://ej.iop.org/images/0025-5734/26/2/A04/tex_sm_2477_img4.gif/>). The proofs depend on the properties of equimeasurable functions, which were applied by Ul'janov in the theory of the embedding of certain classes for (MR 37
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