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Least Squares Approximation of Completely Monotonic Functions by Sums of Exponentials
SIAM Journal on Numerical Analysis, 1979We consider the approximation of a given completely monotonic function $F(t)$ by an exponential sum $Y(t) = a_1 \exp ( - \lambda t) + \cdots + a_n \exp ( - \lambda _n t)$ using the $L_2 $-norm associated with a suitable measure $d\mu (t)$. A best approximation exists and is characterized by a generalized version of the Aigrain–Williams equations ...
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IEEE Transactions on Evolutionary Computation, 2008
An important strength of learning classifier systems (LCSs) lies in the combination of genetic optimization techniques with gradient-based approximation techniques. The chosen approximation technique develops locally optimal approximations, such as accurate classification estimates, Q-value predictions, or linear function approximations.
Martin V. Butz +2 more
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An important strength of learning classifier systems (LCSs) lies in the combination of genetic optimization techniques with gradient-based approximation techniques. The chosen approximation technique develops locally optimal approximations, such as accurate classification estimates, Q-value predictions, or linear function approximations.
Martin V. Butz +2 more
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Discrete least squares approximation and prewavelets from radial function spaces
Mathematical Proceedings of the Cambridge Philosophical Society, 1993AbstractIn this article we study the convergence behaviour of least squares approximations of various types by radial basis functions, i.e. least squares approximations from spaces spanned by radially symmetric functions φ (‖· −xj‖). Here the xj are given ‘centres’ in ℝn which we assume to lie on a grid.
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Least squares approximation to lognormal sum distribution via piecewise linear functions
2009 4th IEEE Conference on Industrial Electronics and Applications, 2009In this paper, the least squares approximation via a piecewise linear function approach is applied to solve the approximation problem of a sum of lognormal random variables. A number of linear basis functions are applied and the corresponding coefficients are specified to form a piecewise linear approximation to the sum lognormal cumulative ...
Lian Zhao, Jiu Ding
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Approximations to complementary error function by method of least squares
Proceedings of the IEEE, 1982A few simple approximations are derived for erfc (x) by method of least squares (MLS). The detailed error profiles are presented. It is shown how these approximations are useful in extracting the inverse of erfc(x). Finally a simple approximation with overall relative root mean square error (RRMS) of less than one percent is presented.
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A new least-square approximation function for analog and digital filtering applications
ISSCS 2011 - International Symposium on Signals, Circuits and Systems, 2011In this paper is presented a new approximation function, based on a least-squares function, which minimizes the loss at the passband. With the proposed function are maximized the loss at the stopband. This optimization produces imaginary zeros, which makes it closer to the ideal function of a brick-wall filter. Comparisons are made with other classical
Calisto Schwedersky, Sidnei Noceti Filho
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Random Errors of Derivatives Obtained from Least Squares Approximations to Empirical Functions
SIAM Review, 1966Untersucht wird der Einfluß von zufälligen Fehlern in den Stützwerten einer äquidistant tabellierten Funktion auf die Werte der ersten beiden Ableitungen, die auf Grund von approximierenden Funktionen berechnet werden. Zur Approximation nach kleinsten Quadraten werden orthogonale Funktionen verwendet.
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Bezoutians Applied to Least Squares Approximation of Rational Functions
2010A projection method to reduce large scale discrete systems which has been introduced in au][12, 21] will be generalized to continues systems without to transform it bilinear. To achieve that goal depending on an algebraic curve γ { ℂ and a rational function h ∈ ℂ(z) a non negative function F: ℂm » ℝ is introduced whose minimizer provides an approximant
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Asymptotic results on nonlinear approximation of regression functions and weighted least squares
Series Statistics, 1980Asymptotic results are given for approximated weighted least squares estimators in nonlinear regression with independent but not necessarily identically distributed errors .
Bunke, H., Schmidt, W. H.
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Functional approximation by feed-forward networks: a least-squares approach to generalization
IEEE Transactions on Neural Networks, 1994This paper considers a least-squares approach to function approximation and generalization. The particular problem addressed is one in which the training data are noiseless and the requirement is to define a mapping that approximates the data and that generalizes to situations in which data samples are corrupted by noise in the input variables.
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