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Relevant bibliographies by topics / Quadrature de Gauss

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Academic literature on the topic 'Quadrature de Gauss'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Quadrature de Gauss"

1

Kwon, Young-Doo, Soon-Bum Kwon, Bo-Kyung Shim, and Hyun-Wook Kwon. "Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/471731.

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This study examined the characteristics of a variable three-point Gauss quadrature using a variable set of weighting factors and corresponding optimal sampling points. The major findings were as follows. The one-point, two-point, and three-point Gauss quadratures that adopt the Legendre sampling points and the well-known Simpson’s 1/3 rule were found to be special cases of the variable three-point Gauss quadrature. In addition, the three-point Gauss quadrature may have out-of-domain sampling points beyond the domain end points. By applying the quadratically extrapolated integrals and nonlinearity index, the accuracy of the integration could be increased significantly for evenly acquired data, which is popular with modern sophisticated digital data acquisition systems, without using higher-order extrapolation polynomials.

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Fee, Greg. "Gauss-Legendre quadrature." ACM SIGSAM Bulletin 33, no. 3 (September 1999): 26. http://dx.doi.org/10.1145/347127.347443.

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Pranić, Miroslav S., and Lothar Reichel. "Rational Gauss Quadrature." SIAM Journal on Numerical Analysis 52, no. 2 (January 2014): 832–51. http://dx.doi.org/10.1137/120902161.

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FRANJIĆ, IVA, JOSIP PEČARIĆ, and IVAN PERIĆ. "GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE." ANZIAM Journal 52, no. 3 (January 2011): 309–17. http://dx.doi.org/10.1017/s1446181111000721.

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AbstractGeneral three-point quadrature formulas for the approximate evaluation of an integral of a function f over [0,1], through the values f(x), f(1/2), f(1−x), f′(0) and f′(1), are derived via the extended Euler formula. Such quadratures are sometimes called “corrected” or “quadratures with end corrections” and have a higher accuracy than the adjoint classical formulas, which only include the values f(x), f(1/2) and f(1−x) . The Gauss three-point, corrected Simpson, corrected dual Simpson, corrected Maclaurin and corrected Gauss two-point formulas are recaptured as special cases. Finally, sharp estimates of error are given for this type of quadrature formula.

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Reichel, Lothar, Miodrag Spalevic, and Jelena Tomanovic. "Rational averaged gauss quadrature rules." Filomat 34, no. 2 (2020): 379–89. http://dx.doi.org/10.2298/fil2002379r.

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It is important to be able to estimate the quadrature error in Gauss rules. Several approaches have been developed, including the evaluation of associated Gauss-Kronrod rules (if they exist), or the associated averaged Gauss and generalized averaged Gauss rules. Integrals with certain integrands can be approximated more accurately by rational Gauss rules than by Gauss rules. This paper introduces associated rational averaged Gauss rules and rational generalized averaged Gauss rules, which can be used to estimate the error in rational Gauss rules. Also rational Gauss-Kronrod rules are discussed. Computed examples illustrate the accuracy of the error estimates determined by these quadrature rules.

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Cao, Ting, Huo-tao Gao, Chun-feng Sun, Yun Ling, and Guo-bao Ru. "Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System." Mathematical Problems in Engineering 2020 (May 14, 2020): 1–13. http://dx.doi.org/10.1155/2020/1072824.

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A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

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Hagler, Brian A. "Laurent-Hermite-Gauss Quadrature." Journal of Computational and Applied Mathematics 104, no. 2 (May 1999): 163–71. http://dx.doi.org/10.1016/s0377-0427(99)00054-0.

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Villarino, Mark B. "Gauss on Gaussian Quadrature." American Mathematical Monthly 127, no. 2 (January 6, 2020): 125–38. http://dx.doi.org/10.1080/00029890.2020.1680201.

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Peherstorfer, Franz. "Gauss-Tchebycheff quadrature formulas." Numerische Mathematik 58, no. 1 (December 1990): 273–86. http://dx.doi.org/10.1007/bf01385625.

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Milovanović, G. V., M. M. Spalević, and L. J. Galjak. "Kronrod Extensions of Gaussian Quadratures with Multiple Nodes." Computational Methods in Applied Mathematics 6, no. 3 (2006): 291–305. http://dx.doi.org/10.2478/cmam-2006-0016.

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Abstract In this paper, general real Kronrod extensions of Gaussian quadrature formulas with multiple nodes are introduced. A proof of their existence and uniqueness is given. In some cases, the explicit expressions of polynomials, whose zeros are the nodes of the considered quadratures, are determined. Very effective error bounds of the Gauss — Turán — Kronrod quadrature formulas, with Gori — Micchelli weight functions, for functions analytic on confocal ellipses, are derived.

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Dissertations / Theses on the topic "Quadrature de Gauss"

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Tang, Tunan. "Extensions of Gauss, block Gauss, and Szego quadrature rules, with applications." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460403903.

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Alqahtani, Hessah Faihan. "GAUSS-TYPE QUADRATURE RULES, WITH APPLICATIONSIN LINEAR ALGEBRA." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1521760018029109.

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Assoufi, Abdelaziz. "Les formules de quadrature numérique dans un domaine de IR2 ou IR3." Pau, 1985. http://www.theses.fr/1985PAUUA001.

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Barajas, Freddy Hernandez. "Modelos multiníveis Weibull com efeitos aleatórios." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-07052013-203915/.

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Os modelos multiníveis são uma classe de modelos úteis na análise de bases de dados com estrutura hierárquica. No presente trabalho propõem-se os modelos multiníveis com resposta Weibull, nos quais são considerados interceptos aleatórios na modelagem dos dois parâmetros da distribuição da variável resposta. Os modelos aqui propostos são flexíveis devido a que a distribuição dos interceptos aleatórios pode der escolhida entre uma das seguintes quatro distribuições: normal, log--gama, logística e Cauchy. Uma extensão dos modelos é apresentada na qual é possível incluir na parte sistemática dos dois parâmetros da distribuição da variável resposta interceptos e inclinações aleatórias com distribuição normal bivariada. A estimação dos parâmetros é realizada pelo método de máxima verossimilhança usando a quadratura de Gauss--Hermite para aproximar a função de verossimilhança. Um pacote em linguagem R foi desenvolvido especialmente para a estimação dos parâmetros, predição dos efeitos aleatórios e para a obtenção dos resíduos nos modelos propostos. Adicionalmente, por meio de um estudo de simulação foi avaliado o impacto nas estimativas dos parâmetros do modelo ao assumir incorretamente a distribuição dos interceptos aleatórios.
Multilevel models are a class of models useful in the analysis of datasets with hierarchical structure. In the present work we propose multilevel Weibull models in which random intercepts are considered to model the two parameters of the Weibull distribution. The proposed models are flexible due to random intercepts distribution can be chosen from one of the four following distributions: normal, log-gamma, logistics and Cauchy. An extension of the models is presented in which we can include, in the systematic part of the two parameters of the distribution, random intercepts and slopes with a bivariate normal distribution. The parameter estimation is performed by maximum likelihood method using the Gauss Hermite quadrature to approximate the likelihood function. A package in R language was especially developed to obtain parameter estimation, random effects predictions and residuals for the proposed models. Additionally, through a simulation study we investigated the misspecification random effect distribution on estimated parameter for the proposed model

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Pujet, Alphonse Christophe. "Des quadratures Suivi de Sur les mouvements simultanés d'un système de points matériels assujettis à rester constamment dans un plan passant par l'origine des coordonnées /." Paris : Bibliothèque universitaire Pierre et Marie Curie (BUPMC), 2009. http://jubil.upmc.fr/sdx/pl/toc.xsp?id=TH_000277_001&fmt=upmc&idtoc=TH_000277_001-pleadetoc&base=fa.

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Ezzirani, Abdelkrim. "Construction de formules de quadrature pour des systèmes de Tchebyshev avec applications aux méthodes spectrales." Pau, 1996. http://www.theses.fr/1996PAUU3035.

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L'objectif principal de cette thèse est la construction des éléments spectraux, qui assureront la condensation de la matrice de masse, c'est à dire une opération conduisant à remplacer cette matrice, sans nuire à la précision des calculs. Cette propriété est très importante lorsque l'approximation est une étape de la résolution numérique d'un problème non stationnaire. On aboutit alors à des schémas réellement explicites, après discrétisation en temps, et ceci sans inverser la matrice de masse. L'idée clef de cette démarche repose sur l'utilisation de nouvelles formules de quadrature bien adaptées à ce type de problèmes. On présente aussi un algorithme pour la construction de formules de quadrature de type Gauss pour les fonctions splines et on mène notamment une étude comparative avec des méthodes existantes.

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Guessab, Allal. "Sur les formules de quadrature numérique à nombre minimal de noeuds dans un domaine de IR(n)." Pau, 1987. http://www.theses.fr/1988PAUU3011.

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Ce travail a pour objet la recherche, à partir de la théorie des polynomes orthogonaux, de conditions permettant l'obtention de formules de quadrature numérique sur des domaines de r(n), avec fonction poids, à nombre minimal de noeuds et exactes sur les espaces r(k(1),k(2),. . . ,k(n)) (d) de degré inférieur ou égal à k(i) par rapport à la variabilité x(i).

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Kzaz, Mustapha. "Accélération de la convergence de la formule de quadrature de Gauss-Jacobi dans le cas des fonctions analytiques." Lille 1, 1992. http://www.theses.fr/1992LIL10174.

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La méthode de quadrature de gauss est une méthode numérique d'intégration très puissante. Néanmoins, elle présente certains inconvénients : la suite générée par cette méthode ne vérifie aucune relation de récurrence, le calcul de chaque terme de cette suite est assez couteux, et enfin, la convergence de cette suite est tres lente lorsque la fonction à intégrer présente des singularités assez voisines de l'intervalle d'intégration. Afin de remédier a ce problème, nous allons proposer des algorithmes d'accélération nous permettant d'avoir une meilleure approximation de la valeur exacte de l'intégrale. Comme dans toutes les méthodes d'extrapolation, on aura à déterminer le ou les premiers termes du développement asymptotique de l'erreur. Dans le premier chapitre, des résultats concernant l'expression de l'erreur, les polynomes orthonormaux de jacobi, ainsi que certains résultats d'analyse seront presentés. Dans le deuxieme et le troisieme chapitre, on etudiera les cas ou l'integrand appartient à certaines classes de fonctions. Dans le dernier chapitre, le cas des intégrales à valeur principale de cauchy sera étudié pour le cas de fonctions étudiées dans les deux chapitres précédents

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MOURA, Márcio José das Chagas. "Novel and faster ways for solving semi-markov processes: mathematical and numerical issues." Universidade Federal de Pernambuco, 2009. https://repositorio.ufpe.br/handle/123456789/4939.

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Made available in DSpace on 2014-06-12T17:35:03Z (GMT). No. of bitstreams: 2 arquivo3630_1.pdf: 2374215 bytes, checksum: 64f9cdc75ffa8167dff3140c0b1e48a2 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009
Petróleo Brasileiro S/A
Processos semi-Markovianos (SMP) contínuos no tempo são importantes ferramentas estocásticas para modelagem de métricas de confiabilidade ao longo do tempo para sistemas para os quais o comportamento futuro depende dos estados presente e seguinte assim como do tempo de residência. O método clássico para resolver as probabilidades intervalares de transição de SMP consiste em aplicar diretamente um método geral de quadratura às equações integrais. Entretanto, esta técnica possui um esforço computacional considerável, isto é, N2 equações integrais conjugadas devem ser resolvidas, onde N é o número de estados. Portanto, esta tese propõe tratamentos matemáticos e numéricos mais eficientes para SMP. O primeiro método, o qual é denominado 2N-, é baseado em densidades de frequência de transição e métodos gerais de quadratura. Basicamente, o método 2N consiste em resolver N equações integrais conjugadas e N integrais diretas. Outro método proposto, chamado Lap-, é baseado na aplicação de transformadas de Laplace as quais são invertidas por um método de quadratura Gaussiana, chamado Gauss Legendre, para obter as probabilidades de estado no domínio do tempo. Formulação matemática destes métodos assim como descrições de seus tratamentos numéricos, incluindo questões de exatidão e tempo para convergência, são desenvolvidas e fornecidas com detalhes. A efetividade dos novos desenvolvimentos 2N- e Lap- serão comparados contra os resultados fornecidos pelo método clássico por meio de exemplos no contexto de engenharia de confiabilidade. A partir destes exemplos, é mostrado que os métodos 2N- e Lap- são significantemente menos custosos e têm acurácia comparável ao método clássico

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Roman, Jean. "Complexité d'algorithmes de séparation de graphes pour des implémentations séquentielles et réparties de l'élimination de Gauss." Bordeaux 1, 1987. http://www.theses.fr/1987BOR10582.

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En appliquant l'etude de l'elimination de gauss a la resolution de grands systemes creux d'equations lineaires, on introduit un solveur par blocs pour lequel on demontre des resultats de complexite en temps et en espace. La methode etant de type "diviser pour gagner", elle induit un parallelisme naturel, etudie dans une deuxieme partie. Une implementation repartie a faible couplage du solveur par blocs pour un calculateur de type "message passing" est proposee

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Books on the topic "Quadrature de Gauss"

1

Evans, Michael J. Sampling from Gauss rules. Toronto: University of Toronto, Dept. of Statistics., 1985.

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Hohmann, Andreas. Inexact Gauss Newton methods for parameter dependent nonlinear problems. Aachen: Shaker, 1994.

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Chhikara, Raj S. The inverse Gaussian distribution: Theory, methodology, and applications. New York: M. Dekker, 1989.

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Góra, Poland) Ogólnopolska Szkoła Historii Matematyki (14th 2000 Zielona. Matematyka czasów Gaussa: XIV Ogólnopolska Szkoła Historii Matematyki. Zielona Góra: Wyższa Szkoła Pedagogiczna im.Tadeusza Kotarbińskiego, 2001.

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Succi, Sauro. The Hermite–Gauss Route to LBE. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0015.

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This chapter describes the side-up approach to Lattice Boltzmann, namely the formal derivation from the continuum Boltzmann-(BGK) equation via Hermite projection and subsequent evaluation of the kinetic moments via Gauss–Hermite quadrature. From a slightly different angle, one may also interpret the Gauss–Hermite quadrature as an optimal sampling of velocity space, or, better still, an exact sampling of the bulk of the distribution function, the one contributing most to the lowest order kinetic moments (frequent events). Capturing higher–order moments, beyond hydrodynamics (rare events), requires an increasing number of nodes and weights.

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Gautschi, Walter. Orthogonal Polynomials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198506720.001.0001.

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This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

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Wearing Gausss Jersey. Taylor & Francis Inc, 2013.

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1952-, Bernhard Robert, and United States. National Aeronautics and Space Administration., eds. A study of methods to predict and measure the transmission of sound through the walls of light aircraft: Integration of certain singular boundary element integrals for applications in linear acoustics. [Washington, DC: National Aeronautics and Space Administration, 1985.

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1952-, Bernhard Robert, and United States. National Aeronautics and Space Administration, eds. A study of methods to predict and measure the transmission of sound through the walls of light aircraft: Integration of certain singular boundary element integrals for applications in linear acoustics. [Washington, DC: National Aeronautics and Space Administration, 1985.

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Book chapters on the topic "Quadrature de Gauss"

1

von Matt, U. "Gauss Quadrature." In Solving Problems in Scientific Computing Using Maple and MATLAB®, 251–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-97953-8_18.

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von Matt, U. "Gauss Quadrature." In Solving Problems in Scientific Computing Using Maple and MATLAB®, 237–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-97619-3_18.

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von Matt, U. "Gauss Quadrature." In Solving Problems in Scientific Computing Using Maple and Matlab ®, 221–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-97533-2_18.

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von Matt, U. "Gauss Quadrature." In Solving Problems in Scientific Computing Using Maple and MATLAB®, 251–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18873-2_18.

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Van Assche, Walter. "Gauss–type quadrature." In Walter Gautschi, Volume 2, 35–49. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7049-6_5.

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Zhang, Guigen. "Gauss Quadrature and Numerical Integration." In Introduction to Integrative Engineering, 269–96. New York : CRC Press, [2017]: CRC Press, 2017. http://dx.doi.org/10.1201/9781315388465-11.

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Rivlin, T. J. "Gauss quadrature for analytic functions." In Orthogonal Polynomials and their Applications, 178–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083358.

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Gautschi, Walter. "Papers on Gauss-type Quadrature." In Walter Gautschi, Volume 2, 633–914. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7049-6_10.

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Gautschi, Walter, and Sotirios E. Notaris. "Newton’s Method and Gauss-Kronrod Quadrature." In International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, 60–71. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6398-8_6.

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Mastroianni, G., and G. Monegato. "Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas." In Approximation and Computation: A Festschrift in Honor of Walter Gautschi, 421–34. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4684-7415-2_28.

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Conference papers on the topic "Quadrature de Gauss"

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Jia, Bin, Ming Xin, and Yang Cheng. "Anisotropic Sparse Gauss-Hermite Quadrature Filter." In AIAA Guidance, Navigation, and Control Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-6618.

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Fousse, Laurent. "Accurate Multiple-Precision Gauss-Legendre Quadrature." In 18th IEEE Symposium on Computer Arithmetic (ARITH '07). IEEE, 2007. http://dx.doi.org/10.1109/arith.2007.8.

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Che, Yanting, Dongze Lv, Jia Luo, Guangming Huang, and Lei Ge. "Dimensionality Reduction Gauss-Hermite Quadrature Filter Algorithm." In 2019 5th International Conference on Control Science and Systems Engineering (ICCSSE). IEEE, 2019. http://dx.doi.org/10.1109/iccsse.2019.00032.

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Husek, Petr, and Jan Stecha. "Nonlinear Kalman Filter by Hermite-Gauss Quadrature." In 2020 20th International Conference on Control, Automation and Systems (ICCAS). IEEE, 2020. http://dx.doi.org/10.23919/iccas50221.2020.9268306.

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Xie, Kai, and Shulin Yang. "Gauss quadrature rule based on parameter estimation." In Seventh International Symposium on Instrumentation and Control Technology, edited by Jiancheng Fang and Zhongyu Wang. SPIE, 2008. http://dx.doi.org/10.1117/12.807496.

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Singh, Abhinoy Kumar, and Shovan Bhaumik. "Nonlinear estimation using transformed Gauss-Hermite quadrature points." In 2013 IEEE International Conference on Signal Processing, Computing and Control (ISPCC). IEEE, 2013. http://dx.doi.org/10.1109/ispcc.2013.6663394.

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Jia, Bin, Ming Xin, and Yang Cheng. "Sparse Gauss-Hermite Quadrature Filter for Orbit Estimation." In AIAA Guidance, Navigation, and Control Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-7588.

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Kejia Pan. "Correction of Gauss Legendre quadrature over a triangle." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002583.

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Oloro, O. J., and E. Okoh. "Computation Of Dimensionless Pressure In A Vertical Well Using Gauss-Chebyshev Quadrature, Gauss-Kronrod Quadrature And Runge-Kutta Fourth Order." In SPE Nigeria Annual International Conference and Exhibition. Society of Petroleum Engineers, 2015. http://dx.doi.org/10.2118/178274-ms.

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Marques da Silva, R. Pitanga, and A. Faro Orlando. "Metrological Considerations on Ultrasonic Flowmeters." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38942.

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An ultrasonic flowmeter is a non-intrusive device that employs the transit time of an ultrasonic signal to measure gas and liquid flow rate. With no moving parts, they are extensively used to measure the flow rates of hydrocarbon gases in applications that require a wide range of pressure (e.g.: custody transfer of natural gas). But despite many technological advances, ultrasonic meters still need metrological assessment. Velocity profiles—fundamental to calculate flow rates—are constructed by making use of the well-known Gauss’ integration technique that depends, to a large extent, on a suitable choice of an orthogonal polynomial. The Gauss-Legendre’s quadrature is the most popular among manufacturers. In order to reduce uncertainties when the velocity profile has few points, the discretization error must be quantified. The paper presents simulations made with Gauss’ and Chebyshev’s quadratures for turbulent flow in smooth pipes and compares them with the theoretical profile. Some aspects of metrological reliability of ultrasonic meters are also discussed.

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Reports on the topic "Quadrature de Gauss"

1

Hybrid gauss-trapezoidal quadrature rules. Gaithersburg, MD: National Institute of Standards and Technology, 1996. http://dx.doi.org/10.6028/nist.ir.5048.

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