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Dissertations / Theses on the topic 'Chebyshev approximation'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Park, Jae H. "Chebyshev Approximation of Discrete polynomials and Splines." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/30195.

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The recent development of the impulse/summation approach for efficient B-spline computation in the discrete domain should increase the use of B-splines in many applications. Because we show here how the impulse/summation approach can also be used for constructing polynomials, the approach with a search table approach for the inverse square root operation allows an efficient shading algorithm for rendering an image in a computer graphics system. The approach reduces the number of multiplies and makes it possible for the entire rendering process to be implemented using an integer processor. In

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2

Chit, Nassim N. "Weighted Chebyshev complex-valued approximation for FIR digital filters." Thesis, Swansea University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278340.

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3

Taylor, Barbara J. "Chebyshev centers and best simultaneous approximation in normed linear spaces." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63872.

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4

Pachon, Ricardo. "Algorithms for polynomial and rational approximation." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:f268a835-46ef-45ea-8610-77bf654b9442.

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Robust algorithms for the approximation of functions are studied and developed in this thesis. Novel results and algorithms on piecewise polynomial interpolation, rational interpolation and best polynomial and rational approximations are presented. Algorithms for the extension of Chebfun, a software system for the numerical computation with functions, are described. These algorithms allow the construction and manipulation of piecewise smooth functions numerically with machine precision. Breakpoints delimiting subintervals are introduced explicitly, implicitly or automatically, the latter metho

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5

Filip, Silviu-Ioan. "Robust tools for weighted Chebyshev approximation and applications to digital filter design." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN063/document.

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De nombreuses méthodes de traitement du signal reposent sur des résultats puissants d'approximation numérique. Un exemple significatif en est l'utilisation de l'approximation de type Chebyshev pour l'élaboration de filtres numériques.En pratique, le caractère fini des formats numériques utilisés en machine entraîne des difficultés supplémentaires pour la conception de filtres numériques (le traitement audio et le traitement d'images sont deux domaines qui utilisent beaucoup le filtrage). La majorité des outils actuels de conception de filtres ne sont pas optimisés et ne certifient pas non plus

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6

Melkemi, Khaled. "Orthogonalité des B-splines de Chebyshev cardinales dans un espace de Sobolev pondéré." Phd thesis, Université Joseph Fourier (Grenoble), 1999. http://tel.archives-ouvertes.fr/tel-00004843.

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Ce travail porte sur l'étude théorique et numérique des splines de Chebyshev. Ces fonctions généralisent les splines polynomiales tout en préservant l'essentiel de leurs propriétés. Elles offrent de plus un intérêt particulier pour le design géométrique grâce aux paramètres de forme qu'elles fournissent. Dans un premier temps, nous étudions les splines basées sur un espace de Chebyshev invariant par translations, et les propriétés de la B-spline correspondante. Dans un deuxième temps, nous montrons, sous certaines hypothèses, que la base des B-splines de Chebyshev est orthonormale dans un espa

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7

Nudo, Frederico. "Approximations polynomiales et méthode des éléments finis enrichis, avec applications." Electronic Thesis or Diss., Pau, 2024. http://www.theses.fr/2024PAUU3067.

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Un problème très courant en science computationnelle est la détermination d'une approximation, dans un intervalle fixe, d'une fonction dont les évaluations ne sont connues que sur un ensemble fini de points. Une approche courante pour résoudre ce problème repose sur l'interpolation polynomiale. Un cas d'un grand intérêt pratique est celui où ces points suivent une distribution équidistante dans l'intervalle considéré. Dans ces hypothèses, un problème lié à l'interpolation polynomiale est le phénomène de Runge, caractérisé par une augmentation de l'erreur d'interpolation près des extrémités de

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8

Johnson, William Joel Dietmar. "Rational fraction approximations for passive network functions." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001083.

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9

Masson, Yannick. "Existence et construction de réseaux de Chebyshev avec singularités et application aux gridshells." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1144/document.

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Les réseaux de Chebyshev sont des systèmes de coordonnées sur les surfaces que l'on obtient par cisaillement d'un domaine du plan. Ceux-ci sont utilisés en particulier pour modéliser les gridshells qui constituent une construction architecturale notamment reconnue pour son faible coût environnemental. La difficulté principale dans la conception des gridshells est le manque de diversité des formes accessibles. En effet, bien que toute surface admette localement en tout point un réseau de Chebyshev, l'existence globale de ce type de coordonnées n'est possible que sur un ensemble restreint de sur

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10

Essakhi, Brahim. "Modélisation électromagnétique 3D sur une large bande de fréquences par combinaison d'une méthode d'éléments finis et d'une approximation par fractions rationnelles : application aux structures rayonnantes." Paris 11, 2005. http://www.theses.fr/2005PA112151.

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Les outils de simulation numérique connaissent une utilisation intensive dans la résolution des problèmes de CEM. L'une des raisons est que la complexité croissante des problèmes à étudier rend l'expérimentation difficile à réaliser. De plus, les mesures ne peuvent être faites qu'en un nombre restreint de points de l'espace. La méthode des éléments finis a pour avantages de pouvoir aisément prendre en compte des géométries complexes et des milieux hétérogènes. Elle utilise un maillage conforme, qui s'adapte à la géométrie de la structure analysée et qui permet des raffinements locaux dans les

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11

Midgley, Stuart. "Quantum waveguide theory." University of Western Australia. School of Physics, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0036.

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The study of nano-electronic devices is fundamental to the advancement of the semiconductor industry. As electronic devices become increasingly smaller, they will eventually move into a regime where the classical nature of the electrons no longer applies. As the quantum nature of the electrons becomes increasingly important, classical or semiclassical theories and methods will no longer serve their purpose. For example, the simplest non-classical effect that will occur is the tunnelling of electrons through the potential barriers that form wires and transistors. This results in an increase in

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12

Volkmer, Toni. "Multivariate Approximation and High-Dimensional Sparse FFT Based on Rank-1 Lattice Sampling." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-222820.

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In this work, the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on arbitrary index sets of finite cardinality is considered, where rank-1 lattices are used as spatial discretizations. The approximation of multivariate smooth periodic functions by trigonometric polynomials is studied, based on a one-dimensional FFT applied to function samples. The smoothness of the functions is characterized via the decay of their Fourier coefficients, and various estimates for sampling errors are shown, complemented by numerical tests for up to 25 dimen

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13

Joldes, Mioara Maria. "Approximations polynomiales rigoureuses et applications." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00657843.

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Quand on veut évaluer ou manipuler une fonction mathématique f, il est fréquent de la remplacer par une approximation polynomiale p. On le fait, par exemple, pour implanter des fonctions élémentaires en machine, pour la quadrature ou la résolution d'équations différentielles ordinaires (ODE). De nombreuses méthodes numériques existent pour l'ensemble de ces questions et nous nous proposons de les aborder dans le cadre du calcul rigoureux, au sein duquel on exige des garanties sur la précision des résultats, tant pour l'erreur de méthode que l'erreur d'arrondi.Une approximation polynomiale rigo

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14

Le, Quéré Patrick. "Etude de la transition à l'instationnarité des écoulements de convection naturelle en cavité verticale différentiellement chauffée par méthodes spectrales chebyshev." Poitiers, 1987. http://www.theses.fr/1987POIT2003.

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On developpe un algorithme d'integration des equations bidimensionnelles instationnaires de navier-stokes d'un fluide de bomussinesq qui couple une discretisation spatiale des variables dependantes par approximation spectrale de chebyshev a une discretisation temporelle de type differences-finies du second ordre. Les cavites etudiees ont des rapports de forme de 1 a 10. Suivant le rapport de forme et les conditions aux limites thermiques, il existe trois mecanismes differents de transition a l'instationnarite qui correspondent a des bifurcations de hopf supercritiques

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15

Mason, J. C. "Near-best approximations by Chebyshev polynomials with applications." Thesis, University of Huddersfield, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411894.

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16

Mace, Rob-Roy L. "Reduction of the Gibbs Phenomenon via interpolation using Chebyshev polynomials, filterying, and chebyshev-padé approximations." Huntington, WV : [Marshall University Libraries], 2005. http://www.marshall.edu/etd/descript.asp?ref=.

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17

Bhikkaji, Bharath. "Model Reduction and Parameter Estimation for Diffusion Systems." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4252.

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18

Minsker, Stanislav. "Non-asymptotic bounds for prediction problems and density estimation." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44808.

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This dissertation investigates the learning scenarios where a high-dimensional parameter has to be estimated from a given sample of fixed size, often smaller than the dimension of the problem. The first part answers some open questions for the binary classification problem in the framework of active learning. Given a random couple (X,Y) with unknown distribution P, the goal of binary classification is to predict a label Y based on the observation X. Prediction rule is constructed from a sequence of observations sampled from P. The concept of active learning can be informally characterized as f

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19

Levesley, Jeremy. "A study of Chebyshev weighted approximations to the solution of Symm's integral equation for numerical conformal mapping." Thesis, Coventry University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304879.

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20

Urban, Lukáš. "Laboratorní úloha zaměřená na obvody se spínanými kapacitory." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2009. http://www.nusl.cz/ntk/nusl-217788.

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This Master`s thesis is focused on through acquaintance of principles of the function circuits with switched capaticors and posibility of their application mainly in frequency filters or signal generators. The origin of the switched capacitor circuits is mentioned at the beginning of the work. There are references to the first scientific work and scientists who have dealt with this issue. Maxwell`s idea: lossy element (resistor) replace with lossless element (switched capacitor) in electric circuit, is further described. In the next chapter of this work are listed types of switching capacitors

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21

LING, MING-XING, and 林明興. "Quadrature mirror filter design by Chebyshev approximation." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/49760218487555791989.

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22

Liu, Yu-Chen, and 劉育成. "Rational Chebyshev Approximation and Generalized Fractional Programs." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/62033766952873260845.

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碩士<br>國立嘉義大學<br>應用數學系研究所<br>98<br>Rational Chebyshev approximation is used to find a rational function to approximate a given continuous function. Rational Chebyshev approximation is also an application of the generalized fractional programs which can be solved by Dinkelbach-type algorithm. Besides rational Chebyshev approximation, Pad'e fractional approximation also can produce a fractional function which approximate to the given continuous function. We implement Dinkelbach-type algorithm for solving rational Chebyshev approximation in Matlab and compare it with Pad'e approximation from numer

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23

CHEN, XIANGKUN. "DESIGN OF OPTIMAL DIGITAL FILTERS (APPROXIMATION, CHEBYSHEV, LINEAR PHASE, MINIMUM PHASE, COMPLEX DOMAIN)." Thesis, 1986. http://hdl.handle.net/1911/15961.

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Four methods for designing digital filters optimal in the Chebyshev sense are developed. The properties of these filters are investigated and compared. An analytic method for designing narrow-band FIR filters using Zolotarev polynomials, which are extensions of Chebyshev polynomials, is proposed. Bandpass and bandstop narrow-band filters as well as lowpass and highpass filters can be designed by this method. The design procedure, related formulae and examples are presented. An improved method of designing optimal minimum phase FIR filters by directly finding zeros is proposed. The zeros off th

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24

Chang, Hsin-Chih, and 張信志. "A New WLS Chebyshev Approximation Method for the Design of IIR Digital Filters." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/83373246513680110483.

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碩士<br>國立清華大學<br>電機工程研究所<br>82<br>This thesis proposes a new approximation method using the weighted least squares (WLS) algorithm for the design of IIR filters. The WLS algorithm used by Chi and Chiou's approxima- tion method for the design of FIR filters is modified for the designed of IIR filters. When the desired frequency response including magnitude and phase is specified, the designed IIR filter is nearly equiripple in absolute (complex) approxima- tion error, but it is not guaranteed

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25

Liu, Yi. "Exact minimax wavelet designs for discrimination /." 2004.

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26

Bani, Younes Ahmad H. "Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics." Thesis, 2013. http://hdl.handle.net/1969.1/151375.

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We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems a

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27

郭永田. "A new self-initated optimum WLS chebyshev approximation method for the design of linear phase fir digital filters." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/18215789495672715919.

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28

Wolfkill, Karlan Stephen. "Pseudo-spectral approximations of Rossby and gravity waves in a two-Layer fluid." Thesis, 2012. http://hdl.handle.net/1957/30138.

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The complexity of numerical ocean circulation models requires careful checking with a variety of test problems. The purpose of this paper is to develop a test problem involving Rossby and gravity waves in a two-layer fluid in a channel. The goal is to compute very accurate solutions to this test problem. These solutions can then be used as a part of the checking process for numerical ocean circulation models. Here, Chebychev pseudo-spectral methods are used to solve the governing equations with a high degree of accuracy. Chebychev pseudo-spectral methods can be described in the following way:

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29

Dostalík, Mark. "Vliv materiálových parametrů na stabilitu termální konvekce." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346943.

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The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear sta

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