We have developed in this paper a morphological disambiguation hybrid system for the Arabic language that identifies the stem, lemma and root of a given sentence words. Following an out-of-context analysis performed b...
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We have developed in this paper a morphological disambiguation hybrid system for the Arabic language that identifies the stem, lemma and root of a given sentence words. Following an out-of-context analysis performed by the morphological analyser Alkhalil Morpho Sys, the system first identifies all the potential tags of each word of the sentence. Then, a disambiguation phase is carried out to choose for each word the right solution among those obtained during the first phase. This problem has been solved by equating the disambiguation issue with a surface optimization problem of spline functions. Tests have shown the interest of this approach and the superiority of its performances compared to those of the state of the art.
A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling proces...
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A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling processes with hard and/or coupled nonlinearities. With an appropriate transformation, the nonlinear models are parameterized such that the nonlinear identification problem is converted into a linear one. The persistently exciting condition for the transformed input is derived to ensure the estimates are consistent with the true system. A simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches based on polynomials. (C) 2006 Elsevier Ltd. All rights reserved.
The contribution of this work is twofold: the authors developed an accurate model to solve the vector wave equation of radially-layered inhomogeneous waveguides based on spline function expansions and automated grid c...
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The contribution of this work is twofold: the authors developed an accurate model to solve the vector wave equation of radially-layered inhomogeneous waveguides based on spline function expansions and automated grid construction by genetic programming, and thenemployed this model to analyse the propagation of electromagnetic waves within oil wells. The developed model uses a spline expansion of the fields to convert the wave equation into a quadratic eigenvalue problem where eigenvectors represent the coefficients of the splines and eigenvalues represent the propagation constant of the eigenmode. The present study compared the proposed model using the classical winding number technique. The results obtained for the first eigenmodes of a typical oil well geometry were more accurate than those obtained by the winding number method. Moreover, the authors model could find a larger amount of eigenmodes for a fixed azimuthal parameter than the standard approach.
Purpose - The paper aims to propose the use of spline functions for the description and visualization of discrete informetric data. Design/methodology/approach - Interpolating cubic splines: are interpolating function...
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Purpose - The paper aims to propose the use of spline functions for the description and visualization of discrete informetric data. Design/methodology/approach - Interpolating cubic splines: are interpolating functions (they pass through the given data points);are cubic, i.e. are polynomials of third degree;have first and second derivatives in the data points, implying that they connect data points in a smooth way;satisfy a best-approximation property which tends to reduce curvature. These properties are illustrated in the paper using real citation data. Findings - The paper reveals that calculating splines yields a differentiable function that still captures small but real changes. It offers a middle way between connecting discrete data by line segments and providing an overall best-fitting curve. Research limitations/implications - The major disadvantage of the use of splines is that accurate data are essential. Practical implications - spline functions can be used for illustrative as well as modelling purposes. Originality/value - splines have hardly ever been used or studied in the information sciences.
We present in this article the structural and algebraic properties of the linear operators generated by C(k) spline functions. These operators are commonly encountered in most numerical applications of linear dynamica...
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We present in this article the structural and algebraic properties of the linear operators generated by C(k) spline functions. These operators are commonly encountered in most numerical applications of linear dynamical systems. A program written in Reduce, which computes these operators, is presented in the Appendix.
Publishing December 2024This book is a continuation of the author's earlier book spline functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the ...
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ISBN:
(数字)9781611978186
ISBN:
(纸本)9781611978179
Publishing December 2024
This book is a continuation of the author's earlier book spline functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the last ten years that make use of splines to approximate functions and data and to solve boundary-value problems. The first half of the book works with bivariate spaces of splines defined on H-triangulations, T-meshes, and curved triangulations. Trivariate tensor-product splines and splines on tetrahedral partitions are also discussed. The second half of the book makes use of these spaces to solve boundary-value problems, with a special emphasis on elliptic PDEs defined on curved domains. The book contains numerous examples and figures to illustrate the methods and their performance.
In addition to the included bibliography, a 125-page list of additional references can be downloaded from the SIAM website.
All of the algorithms in the book have been coded in MATLAB and are included in a package that can also be downloaded from the website. It can be used to run all of the examples in the book. The package also provides an extensive toolbox of functions that readers can utilize to develop their own spline software.
Error bounds for simultaneous approximation of stochastic processes by means of spline functions are derived. As opposed to conventional methods, conditions such as regularity of covariances, stationarity, continuity ...
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Error bounds for simultaneous approximation of stochastic processes by means of spline functions are derived. As opposed to conventional methods, conditions such as regularity of covariances, stationarity, continuity of sample paths, etc. can be dropped, and the error bounds are valid with respect to arbitrary norms. Several applications are indicated: simulating solutions of some stochastic differential equations, computing distributions of continuous functionals by simulation as well as interpolation, numerical differentiation, and numerical integration of stochastic processes by splines.
This paper describes a technique for computing spline function approximations to the solution of two-point boundary-value problems. A performance index that measures the meansquare error in the differential system is ...
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This paper describes a technique for computing spline function approximations to the solution of two-point boundary-value problems. A performance index that measures the meansquare error in the differential system is employed, and this yields a mathematical programming problem in the parameters characterizing the spline function. The gradients of the performance index and constraint functions with respect to these parameters are evaluated, and a numerical solution is then obtained using standard gradient projection algorithms. Computational results confirm the feasibility of this approach and show that good approximations are obtained with spline functions having relatively few knots. It appears that this new technique is very competitive with existing algorithms, especially for problems where the differential system is nonlinear but the boundary restraints are linear.
To investigate errors in astronomical measurements Lobachevsky introduced in 1842 an infinite sequence of univariate spline functions with equally spaced knots, whom classic B-splines are directly connected to. A rema...
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To investigate errors in astronomical measurements Lobachevsky introduced in 1842 an infinite sequence of univariate spline functions with equally spaced knots, whom classic B-splines are directly connected to. A remarkable property is the convergence of the sequences of the Lobachevsky splines and of their derivatives to the normal (or Gaussian) density function and to its derivatives, respectively. This fact suggests to consider Lobachevsky splines for applications to univariate and multivariate scattered interpolation. First, this paper attempts to gather the most significant properties of Lobachevsky splines, generally sparse in the literature, maintaining for convenience a probabilistic setting. Then, applications to interpolation are discussed and numerical experiments, which show an interesting approximation performance, are given.
The problem of computing spline approximation functions taking into account the possibility of optimizing the location of spline nodes is considered. Algorithms are developed to compute spline approximation functions ...
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The problem of computing spline approximation functions taking into account the possibility of optimizing the location of spline nodes is considered. Algorithms are developed to compute spline approximation functions with free conditions at the ends of observation intervals, with controlling of splines by the zero and first derivatives at the ends of observation intervals, and with the provision of optimal locations of spline nodes. The results of mathematical modeling of the algorithms for computing spline approximation functions are presented.
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