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Counterexamples in best approximation [PDF]
Proceedings of the American Mathematical Society, 1976 Several counterexamples for approximation to continuous functions by polynomials are given. One example shows that the points of maximum deviation of a continuous real valued function on an interval from its polynomial of degree n
S. J. Poreda
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Canonical Sets of Best L1-Approximation [PDF]
Journal of Function Spaces and Applications, 2012 In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the ...
Dimiter Dryanov, Petar Petrov
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Journal of Approximation Theory, 1993 Let \(M\) be an \(n\)-dimensional Chebyshev subspace of \(C[a,b]\). For \(f\in C[a,b]\) define \(M_ f\) as the set of functions \(p\in M\) such that \(p(x)f(x)\geq 0\) for all \(x\in [a,b]\). Best copositive approximation to \(f\) is the approximation by elements of \(M_ f\). The author develops a theory for best copositive approximation which is quite
Zhong, J.
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Interpolation and best simultaneous approximation
Journal of Approximation Theory, 2010 The paper deals with best simultaneous approximation (b.s.a.) to \(k\) continuous functions on the interval \([a,b]\) from a finite subspace of \(C[a,b]\). The authors establish the limit of the b.s.a., which is important to provides qualitative and approximation analytic information concerning the the b.s.a.
Héctor Cuenya, Fabián E. Levis
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Best comonotone approximation [PDF]
Transactions of the American Mathematical Society, 1994 The authors have described a general theory of best comonotone approximation in \(C[a,b]\) by elements of an \(n\)-dimensional extended Chebyshev subspace. Two theorems on characterizations are studied which seem to be useful for the actual computation of best comonotone approximations.
Deutsch, Frank, Zhong, Jun
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Convergence of Best Best L ∞ -Approximations [PDF]
Proceedings of the American Mathematical Society, 1981 Let ( Ω ,
Abdallah M. Al-Rashed, Richard B. Darst
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Journal of Kufa for Mathematics and Computer, 2017 For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_pâ ...
GHAZI ABDULLAH Madlol
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On Best Simultaneous Approximation
Journal of Approximation Theory, 1997 Let \(X\) be a compact Hausdorff space, \(Y\) be a normed linear space, \(C(X, Y)\) be the vector space of continuous functions from \(X\) to \(Y\) and \(S\) be a subspace of \(C(X, Y).\) Suppose that \(C(X, Y)\) is normed with a given norm \(\| \cdot\| _A\) and that \(U\) is the unit ball of \((\mathbb R^n, \| \cdot\| _B).
Li, Chong, Watson, G.A
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A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization [PDF]
, 2012 Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming).
Gnecco, Giorgio +3 more
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Estimates of the Approximation Error Using Rademacher Complexity: Learning Vector-Valued Functions [PDF]
, 2008 For certain families of multivariable vector-valued functions to be approximated, the accuracy of approximation schemes made up of linear combinations of computational units containing adjustable parameters is investigated.
Gnecco Giorgio +7 more
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