Results 221 to 230 of about 63,156 (266)

Nonlinear approximation

Acta Numerica, 1998
This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come from linear spaces but rather from nonlinear manifolds. The central question to be studied is what, if any, are the advantages of nonlinear approximation over the ...
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Nonlinear Methods of Approximation

Foundations of Computational Mathematics, 2003
This extensive survey paper is, according to its author, complementary to the survey by \textit{R. A. DeVore} [Acta Numerica 7, 51--150 (1998; Zbl 0931.65007)]. The central concept is \(m\)-term approximation, that is, approximation of a given element \(f\) of a Banach space \(X\) by linear combinations of \(\leq m\) elements \(g_k\) taken from some ...
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Discrete Nonlinear Mean Approximation

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977
AbstractBest approximation on a finite set by a non‐linear family of functions with respect to a general sum “norm”, which includes as a special case the Lp norms (1 < p < ∞), is considered. Properties of best approximations are given. It is shown that a local minimum of the error may not be a global minimum. Computation of best approximations is
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Approximations for nonlinear functions

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1992
By applying a version of the Stone-Weierstrass theorem the author shows that a continuous real-valued function on a nonempty compact topological space can be uniformly approximated by a sum of the form \[ a_ 1 e^{\phi(x,p_ 1)}+\cdots+ a_ me^{\phi(x,p_ m)}. \] {}.
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Nonlinear Estimation and Asymptotic Approximations

Econometrica, 1978
central objective of this paper is to present a series expansion of nonlinear estimators in order to facilitate an analysis of the distributions of such estimators. Where the estimator under consideration is a maximum likelihood estimator, the method provides somewhat more information, as well as higher order approximations to the distributions of the ...
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Nonlinear Approximation and Muckenhoupt Weights

Constructive Approximation, 2006
In the general atomic setting of an unconditional basis in a (quasi-) Banach space, we show that representing the spaces of m-terms approximation as Lorentz spaces is equivalent to the verification of two inequalities (Jackson and Bernstein), and that the validity of these two properties is equivalent to the Temlyakov property. The proof is very direct
Kerkyacharian, G., Picard, D.
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Nonlinear Approximation of Random Functions

SIAM Journal on Applied Mathematics, 1997
Summary: Given an orthonormal basis and a certain class \(X\) of vectors in a Hilbert space \(H\), consider the following nonlinear approximation process: approach a vector \(x\in X\) by keeping only its \(N\) largest coordinates, and let \(N\) go to infinity.
Cohen, Albert, D'Ales, Jean-Pierre
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Nonlinear Approximation with Local Fourier Bases

Constructive Approximation, 2000
It is shown that local Fourier bases are unconditional bases for the modulation spaces on \(R\), including the Bessel potential spaces and the Segal algebra \(S_0\). As a consequence, the abstract function spaces that are defined by the approximation properties with respect to a local Fourier basis, are precisely the modulation spaces.
Gröchenig, Karlheinz, Samarah, Salti
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Infinite-interval nonlinear approximations

Constructive Approximation, 1988
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kaufman, E. H. jun., Taylor, G. D.
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Nonlinear Operator Approximation

1976
This paper is concerned with convergence theorems and error bounds for approximate solutions of nonlinear problems, with particular applications to Urysohn integral equations. It is an abbreviated version of a more extensive projected sequel by P.M. Anselone, J. Davis and P.M. Prenter.
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