Search results for "Rate of convergence"
showing 10 items of 69 documents
Baseband predistorter using direct spline computation
2005
A baseband predistorter is presented. Key features of the predistorter reside in the use of cubic spline interpolation to generate predistorted input data to the power amplifier, without time convergence problems of classical approaches, with the goal of a reduction in the computational effort. Simulated behaviour of the proposed scheme is presented, demonstrating the effectiveness of the approach.
Thresholding projection estimators in functional linear models
2008
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.
Convergence analysis for hierarchical longitudinal data
2018
Abstract Convergence analysis is typically envisaged either from a macro or a micro perspective. However, empirical tests tend to ignore that the two levels are often “nested” in a hierarchy. Building on hierarchical growth curve modelling, we propose an approach to convergence analysis that allows contemporaneous inference on macro and micro-convergence. Compared to the classic linear convergence analysis, the suggested methodology provides a more flexible alternative to model heterogeneity and validate the results for possible Galton's fallacy. We illustrate the approach in two empirical examples, one considering convergence across European regions and countries and the other across Itali…
Avoiding strange attractors in efficient parametric families of iterative methods for solving nonlinear problems
2019
[EN] Searching zeros of nonlinear functions often employs iterative procedures. In this paper, we construct several families of iterative methods with memory from one without memory, that is, we have increased the order of convergence without adding new functional evaluations. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Moreover, we have found some elements of the family whose behavior includes strange attractors of different kinds that must be avoided in practice. In this sense, Feigenbaum diagrams have resulted an extremely …
Fast Image Restoration Algorithms Based on PDE Models Using Modified Hopfield Neural Network
2010
Two image restoration algorithms based on modified Hop field neural network and variational partial differential equations (PDE) were proposed in our previous work [1, 2]. But the convergence rate of the proposed algorithms was slow. In this paper, we develop a fast update rule based on modified Hop field neural network (MHNN) of continuous state change and two fast image restoration algorithms. Experimental results show that, when compared with the previous algorithms, our proposed algorithms have better performance both in convergence rate and in image restoration quality.
Spectral Density Estimate for Stable Processes Observed with an Additive Error
2018
International audience; In this paper, a symmetric alpha stable process where its spectral representation has an additive error is considered. The error is supposed to be constant. A periodogram as estimator of the spectral density and its rate of convergence are given. In order to give an asymptotically unbiased and consistent estimate of the spectral density, this periodogram is smoothed by an adapted spectral window. The rate of convergence is given.
Mapping discounted and undiscounted Markov Decision Problems onto Hopfield neural networks
1995
This paper presents a framework for mapping the value-iteration and related successive approximation methods for Markov Decision Problems onto Hopfield neural networks, for both discounted and undiscounted versions of the finite state and action spaces. We analyse the asymptotic behaviour of the control sets and we give some estimates on the convergence rate for the value-iteration scheme. We relate the convergence properties on an energy function which represents the key point in mapping Markov Decision Problems onto Hopfield networks. Finally, an application from queueing systems in communication networks is taken into consideration and the results of computer simulation of Hopfield netwo…
Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order.
2011
A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison …
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
1999
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [ A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint,…
Accelerated Proximal Gradient Descent in Metric Learning for Kernel Regression
2018
The purpose of this paper is to learn a specific distance function for the Nadayara Watson estimator to be applied as a non-linear classifier. The idea of transforming the predictor variables and learning a kernel function based on Mahalanobis pseudo distance througth an low rank structure in the distance function will help us to lead the development of this problem. In context of metric learning for kernel regression, we introduce an Accelerated Proximal Gradient to solve the non-convex optimization problem with better convergence rate than gradient descent. An extensive experiment and the corresponding discussion tries to show that our strategie its a competitive solution in relation to p…