The subject of this work is the study of Birkhoff's polynomial interpolation. Given a list Zn=[z0,...,zn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{am...
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The subject of this work is the study of Birkhoff's polynomial interpolation. Given a list Zn=[z0,...,zn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Z_n=[z_recursive,...,z_{n}] $$\end{document} with (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (n+1) $$\end{document} distinct nodes, of K=R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb {K}=\mathbb {R} $$\end{document} or C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb {C} $$\end{document}, we will seek to study the questions of existence and uniqueness of a polynomial P such that P and a number of its derivatives take, in these nodes, given values. Recently, Messaoudi et al. (Numer. algorithms 80, 253-278 2019) presented a new algorithm for computing the Hermite interpolation polynomial called the Generalized recursive Polynomial Interpolation algorithm (GRPIA). In this paper, we will give a new formulation of the Birkhoff polynomial interpolation problem and derive a new algorithm, called the recursive Hermite-Birkhoff Polynomial Interpolation algorithm (RHBPIA), to solve the Birkhoff interpolation problem and generalize the GRPIA. A new existing result will be established. The numerical stability of this algorithm will also be studied and some examples will be given.
In real applications, a time delay in the parameter update of the neural network is sometimes required. In this paper, motivated by the Chebyshev functional link artificial neural network (CFLANN), a new structure bas...
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In real applications, a time delay in the parameter update of the neural network is sometimes required. In this paper, motivated by the Chebyshev functional link artificial neural network (CFLANN), a new structure based on the time delay adaptation is developed for nonlinear system identification. Particularly, we present a new CFLANN-delayed recursive least square (CFLANN-DRLS), as an online learning algorithm for parameter adaptation in CFLANN. The CFLANN-DRLS algorithm exploits the time delayed error signal with the gain vector delayed by D cycles to form the weight increment term, which provides potential implementation in the filter with pipelined structure. However, it suffers from the instability problems under imperfect network delay estimate. To overcome this problem, we further propose a modified CFLANN-DRLS (CFLANN-MDRLS) algorithm by including a compensation term to the error signal. We analyze the stability and convergence of the proposed algorithm. Simulations in nonlinear system identification contexts reveal that the newly proposed CFLANN-MDRLS algorithm can effectively compensate the time delay of system and it is even superior to the algorithm without delay in some cases. (C) 2018 Elsevier B.V. All rights reserved.
Big multi-step wind speed forecasting is hard to be realized due to the high-requirement of the built forecasting models. However, the big multi-step forecasting is expected in the wind power systems, which can provid...
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Big multi-step wind speed forecasting is hard to be realized due to the high-requirement of the built forecasting models. However, the big multi-step forecasting is expected in the wind power systems, which can provide sufficient time for the wind grids to be operated in the emergency cases. In the study, a new hybrid computational framework for the big multi-step wind speed forecasting is proposed, consisting of Wavelet Packet Decomposition (WPD), Elman Neural Networks (ENN), boosting algorithms and Wavelet Packet Filter (WPF). The novelty of the study is to investigate the big multi-step wind speed forecasting performance using various computing strategies in the proposed new hybrid WPD-BoostENN-WPF framework. Four different wind speed time series data are provided to complete the real forecasting experiments. The experimental results indicate that: (a) all of the proposed hybrid models have better performance than the corresponding single forecasting models in the big multi-step predictions. The 9 step MAE errors for the experimental data #1 from the proposed four hybrid forecasting models are only 1.2821 m/s, 1.1276 m/s, 1.1718 m/s and 1.2684 m/s, respectively;(b) the proposed four hybrid forecasting models have no significant forecasting difference;and (c) all of them are suitable for the big multi-step wind speed forecasting. (C) 2018 Elsevier Ltd. All rights reserved.
The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to ...
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The enumeration of all minimal paths between a terminal pair of a given graph is widely used in a lot of applications such as network reliability assessment. In this paper, we present a new and efficient algorithm to generate all minimal paths in a graph G(V, E). The algorithm proposed builds the set of minimal paths gradually, starting from the source node s. We present two versions of our algorithm;the first version determines all feasible paths between a pair of terminals in a directed graph without cycle, and this version runs in linear time O(vertical bar V vertical bar + vertical bar E vertical bar). The second version determines all minimal paths in a general graph (directed and undirected graph). In order to show the process and the effectiveness of our method, an illustrative example is presented for each case.
作者：
Flammang, VUniv Lorraine
Dept Math UMR CNRS IECL 7502 UFR MIM Site Metz3 Rue Augustin FresnelBP 45112 F-57073 Metz 03 France
Thanks to our recursive algorithm developed in [Trace of totally positive algebraic integers and integer transfinite diameter, Math. Comp. 78(266) (2009) 1119-1125], we prove that, if a is a totally positive algebraic...
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Thanks to our recursive algorithm developed in [Trace of totally positive algebraic integers and integer transfinite diameter, Math. Comp. 78(266) (2009) 1119-1125], we prove that, if a is a totally positive algebraic integer of degree d >= 2 with minimum conjugate a l then, with a finite number of explicit exceptions, tr(alpha)/d >=alpha(1) + 1.68.
作者：
Flammang, VUniv Lorraine
UMR CNRS 7502 IECL Dept MathUFR MIM Site Metz3 Rue Augustin FresnelBP 45112 F-57073 Metz 03 France
We consider intervals of the form [r/s, u], where r, s are positive integers with gcd (r, s) = 1 and u is a real number, or of the form [0, (root a - root b)(2)], where a, b are positive integers. Thanks to a lemma of...
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We consider intervals of the form [r/s, u], where r, s are positive integers with gcd (r, s) = 1 and u is a real number, or of the form [0, (root a - root b)(2)], where a, b are positive integers. Thanks to a lemma of Chudnovsky, we give first a lower bound of the integer trans finite diameter of such intervals. Then, using the method of explicit auxiliary functions and our recursive algorithm, we explain how to get an upper bound for this quantity. We finish with some numerical examples. Secondly, we prove inequalities on the integer trans finite diameter of Farey intervals, i.e., intervals of the type [a/q, b/s], where vertical bar as - bq vertical bar = 1.
In this paper, the robust distributed filtering problem is investigated for a class of wireless sensor networks with stochastic parameter and topology uncertainties. The local filters collect information not only from...
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In this paper, the robust distributed filtering problem is investigated for a class of wireless sensor networks with stochastic parameter and topology uncertainties. The local filters collect information not only from itself but also from its neighbouring sensor nodes according to the network topology. A novel robust distributed filter is proposed which takes stochastic parameter and topology uncertainties into full consideration but does not depend on any specific structure of uncertainties. By proper designing of the filter gain, the trace of estimation error covariance is minimised at each time step, where the new stochastic analysis and augmentation transformation techniques are developed to handle the challenges resulting from multiplicative stochastic uncertainties and sparse topology. The corresponding recursive robust distributed filtering algorithm is also presented for real-time online applications. Finally, a simulation study is carried out to illustrate the effectiveness and applicability of our proposed method.
The direct problem of light scattering for a fiber optic Bragg grating is considered. The formulation and solution of the problem based on the transfer-matrix method are discussed. A modification of the method is prop...
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The direct problem of light scattering for a fiber optic Bragg grating is considered. The formulation and solution of the problem based on the transfer-matrix method are discussed. A modification of the method is proposed which reduces it to a computationally convenient universal recursive algorithm similar to the Thomas algorithm. Using the finite volume method in the coupled-mode approximation, the elements of transfer matrices were calculated with local third-order accuracy in coordinate on a nonuniform computational grid. Numerical calculations for the direct scattering problem for a Bragg grating with apodization and nonlinear chirp were performed using the recursive algorithm. Numerical simulations confirmed the significant increase in the accuracy of calculations when solving the scattering problem on a nonuniform grid.
A scattering (S-) parameter method has been proposed for electromagnetic property extraction of a target layer within metal-backed inhomogeneous metamaterial (MM) structures. It relies on recursive S-parameters for tw...
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A scattering (S-) parameter method has been proposed for electromagnetic property extraction of a target layer within metal-backed inhomogeneous metamaterial (MM) structures. It relies on recursive S-parameters for two different polarizations (parallel and perpendicular). Two different algorithms depending on the value of the incidence angles were proposed to add flexibility to our method. The algorithms were first validated by a metal-backed quasi-one-port method applicable only for one-layer (homogeneous) samples. Then, they were applied to extract electromagnetic properties of the split-ring-resonator-wire MM slab of a metal-backed two-layer inhomogeneous structure and the Omega MM slab of a metal-backed four-layer inhomogeneous structure, and extracted properties by our algorithms were compared with those retrieved by different methods applicable for homogeneous samples only. The accuracy of our method was also examined when there was some noise in S-parameters, when there was a misalignment in incidence angles, and a when large value of iteration number was used.
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