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Restricted Nonlinear Approximation
Constructive Approximation, 2000This paper introduces a new form of nonlinear approximation called restricted approximation. It is a generalization of \(n\)-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant.
R A Devore
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Nonlinear Nonnested Spline Approximation
Constructive Approximation, 2016 Linear and in particular non-linear spline approximation is a most useful tool in the approximation of for instance two-dimensional functions. Usually, piecewise polynomial splines with more and more refined knot-sequences are considered as elements of nested spaces spanned by splines. Generalising from this point of view, it is interesting to consider
Lind, Martin, Petrushev, Pencho
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Nonlinear Wavelet Approximation in BMO
Constructive Approximation, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivanov, Kamen G., Petrushev, Pencho
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An Analysis of Approximate Nonlinear Elimination
SIAM Journal on Scientific Computing, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul J. Lanzkron +2 more
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Nonlinear Approximation of Random Functions
SIAM Journal on Applied Mathematics, 1997Summary: 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.
Albert Cohen 0002, Jean-Pierre D'Ales
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Nonlinear Methods of Approximation
Foundations of Computational Mathematics, 2003This 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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Approximations for nonlinear functions
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1992By 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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Minimax nonlinear approximation by approximation on subsets
Communications of the ACM, 1972A possible algorithm for minimax approximation on an infinite set X consists in choosing a sequence of finite point sets { X k } which fill out X and taking a limit of minimax approximations on X
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Nonlinear Approximation and Muckenhoupt Weights
Constructive Approximation, 2006In 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 Estimation and Asymptotic Approximations
Econometrica, 1978central 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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