Results 321 to 330 of about 3,102,564 (352)

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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Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations

, 2008
We investigate mathematically a nonlinear approximation type approach recently introduced in Ammar et al. (J. Non-Newtonian Fluid Mech. 139:153–176, 2006) to solve high-dimensional partial differential equations. We show the link between the approach and
C. Bris, Tony Lelièvre, Yvon Maday
semanticscholar   +1 more source

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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Accurate Approximations for Nonlinear Vibrations

2019
As global issues such as climate change and overpopulation continue to grow, the role of the engineer is forced to adapt. The general population now places an emphasis not only on the performance of a mechanical system, but also the efficiency with which this can be achieved.
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Minimax nonlinear approximation by approximation on subsets

Communications of the ACM, 1972
A 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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Linear and Nonlinear Approximation

1996
Let f be a continuous function on the interval [a, b] ⊂ ℝ |R which is to be approximated by an approximation function Φ ∈ C[a, b]. Φ shall be dependent on x ∈ [a, b] and on certain parameters \( c_0 ,c_1 , \ldots ,c_n \):\( \Phi (x): = \Phi (x,c_0 ,c_1 , \ldots ,c_n ) = \Phi (x,c)\,for c = (c_0 ,c_1 , \ldots ,c_n )^T.
Gisela Engeln-Müllges, Frank Uhlig
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