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Hierarchical Nonlinear Approximation for Experimental Design and Statistical Data Fitting
SIAM Journal on Scientific Computing, 2007This paper proposes a hierarchical nonlinear approximation scheme for scalar-valued multivariate functions, where the main objective is to obtain an accurate approximation with using only very few function evaluations.
D. Busby, C. Farmer, A. Iske
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, 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
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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
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On the convex approximation of nonlinear inequalities
Optimization, 1974The present paper deals with sufficient conditions for a system of convex incqualities to be a local approximation of a given arbitrary system in the following sense: the solution set of the first system is tangential to the solution set of the second one at the point under consideration. a criterion is proposed. For the case, in which the given system
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On the importance of combining wavelet-based nonlinear approximation with coding strategies
IEEE Transactions on Information Theory, 2002This paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory. Contrasting linear and nonlinear approximation spaces, we show that there are interesting classes of functions/random ...
A. Cohen +3 more
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The Mean Green's Function: A Nonlinear Approximation
, 1971In this paper, we examine the behavior of the coherent Green's function in a randomly fluctuating, unbounded, and statistically homogeneous medium. The starting point of the analysis is a ‘nonlinear’ approximation of the Dyson equation which has been ...
S. Rosenbaum
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Nonlinear Approximation of Random Functions
SIAM Journal on Applied Mathematics, 1997Given 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.
A. Cohen, Jean-Pierre D'Ales
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Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
, 1995When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and ...
X. Guan, P. Luh, Lan Zhang
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Nonlinear system approximations
26th IEEE Conference on Decision and Control, 1987We are interested in approximating a nonlinear system by a feedback linearizable system instead of a linear system. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation.
Louis R. Hunt, Richard Goldthwait
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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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A Nonlinear Approximation for the Pressure Behavior of Heterogeneous Reservoirs
, 1993Recent years have seen extensive use of analytical techniques to study pressure behavior in layered, laterally, and radially composite systems.
F. Kuchuk +2 more
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