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Dissertations / Theses on the topic 'Splines'
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Howell, John R. "Analysis Using Smoothing Via Penalized Splines as Implemented in LME() in R." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1702.pdf.
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Schöne, René. "Torische Splines." Duisburg Köln WiKu, 2007. http://d-nb.info/989082741/04.
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Stone, G. "Bivariate splines." Thesis, University of Bath, 1988. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233827.
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Andriamaro, Miangaly Gaelle. "Vector refinable splines and subdivision." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/1747.
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Thesis (MSc (Mathematics))--Stellenbosch University, 2008.In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove some of its properties, thereby building a basis for a later extension to the vector setting. Defining a subdivision scheme associated to the B-spline refinement mask, we then present the proof of a well-known convergence result. Subdivision is a powerful tool used in computer-aided geometric design (CAGD) for the generation of curves and surfaces. The basic step of a subdivision algorithm consists of starting with a given set of points, called the initial control points, and creating new points as a linear combination of the previous ones, thereby generating new control points. Under certain conditions, repeated applications of this procedure yields a continuous limit curve. One important goal of this thesis is to study a particular extension of scalar subdivision to matrix subdivision ...
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Finnigan, Gordon Thomas. "Arbitrary Degree T-Splines." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2453.pdf.
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Gupta, Surendra K. "Parametric splines in tension /." Online version of thesis, 1989. http://hdl.handle.net/1850/10625.
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Faigle, Christopher Tyler. "DMS-Splines and radiosity." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624727.
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Goosen, Karin M. (Karin Michelle). "Subdivision, interpolation and splines." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51924.
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Thesis (MSc)--University of Stellenbosch, 2000.ENGLISH ABSTRACT: In this thesis we study the underlying mathematical principles of stationary subdivision, which can be regarded as an iterative recursion scheme for the generation of smooth curves and surfaces in computer graphics. An important tool for our work is Fourier analysis, from which we state some standard results, and give the proof of one non-standard result. Next, since cardinal spline functions have strong links with subdivision, we devote a chapter to this subject, proving also that the cardinal B-splines are refinable, and that the corresponding Euler-Frobenius polynomial has a certain zero structure which has important implications in our eventual applications. The concepts of a stationary subdivision scheme and its convergence are then introduced, with as motivating example the de Rahm-Chaikin algorithm. Standard results on convergence and regularity for the case of positive masks are quoted and graphically illustrated. Next, we introduce the concept of interpolatory stationary subdivision, in which case the limit curve contains all the original control points. We prove a certain set of sufficient conditions on the mask for convergence, at the same time also proving the existence and other salient properties of the associated refinable function. Next, we show how the analysis of a certain Bezout identity leads to the characterisation of a class of symmetric masks which satisfy the abovementioned sufficient conditions. Finally, we show that specific special cases of the Bezout identity yield convergent interpolatory symmetric subdivision schemes which are identical to choosing the corresponding mask coefficients equal to certain point evaluations of, respectively, a fundamental Lagrange interpolation polynomial and a fundamental cardinal spline interpolant. The latter procedure, which is known as the Deslauriers-Dubuc subdivision scheme in the case of a polynomial interpolant, has received attention in recent work, and our approach provides a convergence result for such schemes in a more general framework. Throughout the thesis, numerical illustrations of our results are provided by means of graphs.
AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die onderliggende wiskundige beginsels van stasionêre onderverdeling, wat beskou kan word as 'n iteratiewe rekursiewe skema vir die generering van gladde krommes en oppervlakke in rekenaargrafika. 'n Belangrike stuk gereedskap vir ons werk is Fourieranalise, waaruit ons sekere standaardresuJtate formuleer, en die bewys gee van een nie-standaard resultaat. Daarna, aangesien kardinale latfunksies sterk bande het met onderverdeling, wy ons 'n hoofstuk aan hierdie onderwerp, waarin ons ook bewys dat die kardinale B-Iatfunksies verfynbaar is, en dat die ooreenkomstige Euler-Frobenius polinoom 'n sekere nulpuntstruktuur het wat belangrike implikasies het in ons uiteindelike toepassings. Die konsepte van 'n stasionêre onderverdelingskema en die konvergensie daarvan word dan bekendgestel, met as motiverende voorbeeld die de Rahm-Chaikin algoritme. Standaardresultate oor konvergensie en regulariteit vir die geval van positiewe maskers word aangehaal en grafies geïllustreer. Vervolgens stelons die konsep van interpolerende stasionêre onderverdeling bekend, in welke geval die limietkromme al die oorspronklike kontrolepunte bevat. Ons bewys 'n sekere versameling van voldoende voorwaardes op die masker vir konvergensie, en bewys terselfdertyd die bestaan en ander toepaslike eienskappe van die ge-assosieerde verfynbare funksie. Daarna wys ons hoedat die analise van 'n sekere Bezout identiteit lei tot die karakterisering van 'n klas simmetriese maskers wat die bovermelde voldoende voorwaardes bevredig. Laastens wys ons dat spesifieke spesiale gevalle van die Bezout identiteit konvergente interpolerende simmetriese onderverdelingskemas lewer wat identies is daaraan om die ooreenkomstige maskerkoëffisientegelyk aan sekere puntevaluasies van, onderskeidelik, 'n fundamentele Lagrange interpolasiepolinoom en 'n kardinale latfunksie-interpolant te kies. Laasgenoemde prosedure, wat bekend staan as die Deslauriers-Dubuc onderverdelingskema in die geval van 'n polinoominterpolant, het aandag ontvang in onlangse werk, en ons benadering verskaf 'n konvergensieresultaat vir sulke skemas in 'n meer algemene raamwerk. Deurgaans in die tesis word numeriese illustrasies van ons resultate met behulp van grafieke verskaf.
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WANG, DONGHUI. "Modelisation de surfaces b-splines s'appuyant sur des courbes de bezier ou b-splines." Paris, ENSAM, 1990. http://www.theses.fr/1989ENAM0009.
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Ce travail concerne l'elaboration d'une methode de modelisation des surfaces b-splines en s'appuyant sur des courbes de bezier ou b-splines predefinies. Il a ete realise successivement chez renault automation et matra datavision, sur le systeme unisurf integre a euclid-is de matra datavision. Le probleme pose est de savoir comment on peut modeliser une surface polynomiale (surface de bezier ou b-spline) sous les contraintes suivantes: la surface obtenue doit respecter l'esthetique et la regularite des sections donnees par l'utilisateur; la methode proposee doit etre simple a utiliser et facile a controler; la surface doit respecter une precision voulue. Pour essayer de la resoudre, nous proposons une methode generale en utilisant le mecanisme de la modelisation des surfaces proposee par les methodes de coons et de gordon, ainsi que la representation mathematique b-spline et ses diverses techniques. L'etude et la realisation de notre probleme peuvent etre examinees selon les aspects suivants: etude de la transformation entre la representation de bezier et la representation b-spline, et elaboration de l'algorithme wm; analyse du mecanisme de la modelisation des surfaces; etablissement d'un type de modelisation des surfaces general
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Jallet, Roxane. "Splines de régression et splines de lissage en régression non paramétrique avec bruit processus." Paris 6, 2008. http://www.theses.fr/2008PA066054.
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Dans ce travail de thèse, nous nous intéressons aux méthodes d’estimation d’une fonction de régression régulière bruitée par un processus, par les splines de lissage et les splines de régression. Dans le cadre du modèle à bruit processus, nous présentons les résultats de convergence asymptotique obtenus pour l’estimateur des splines de lisage et proposons une extension au cas de données déséquilibrées. Afin de construire les estimateurs des splines de régression dans le cadre du modèle à bruit processus, nous introduisons deux critères : les moindres carrés ordinaires et les moindres carrés généralisés. Nous étudions pour ces deux estimateurs des splines de régression, les vitesses de convergence et comparons les résultats obtenus. Enfin, nous mettons en œuvre des simulations pour comparer numériquement les différents estimateursIn the present work, we are interested in estimation methods of a regular function with a processus noise by smoothing splines and regression splines. Convergence rates results for smoothing splines are presented in the case of processus noise and an extension for unbalanced data is proposed. In order to build the regression splines estimators, we introduce two criteria : ordinary least squares and generalized least squares. For these two regression splines estimators convergence rates are studied and compared. Finally, through simulations the various estimators are compared
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Mößner, Bernhard. "B-splines als Finite Elemente /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015210875&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Donovan, George C. "Fractal functions, splines, and wavelet." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30411.
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Minghim, Rosane. "Modelagem de objetos por splines." [s.n.], 1990. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261343.
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Orientador: Clesio Luis TozziDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica
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Resumo: Com o objetivo de tratar o problema de representação de objetos tridimensionais em computação gráfica , este trabalho apresenta um estudo do assunto, destacando a modelagem de sólidos por superfícies matemáticas , uma vez que ela representa uma alternativa útil e flexível de manipulação de objetos. Dois métodos de modelagem superficial são abordados: Bezier e B-spline. Um sistema de modelagem é implementado usando tais métodos, com atenção especial aos aspectos de interação homem/máquina, como a introdução dos dados tridimensionais necessários e visualiza-lo dos objetos projetados. O desenvolvimento do sistema é baseado em técnicas de Engenharia de Software, selecionadas para resolução desse tipo de problema
Abstract: Dealing with the problem of object representation in Computer Graphics, this paper presents a review of the literature on the subject highlighting the mIodeling of solid objects through Mathematical Surfaces, as this shows up as a usefull and flexible alternative to solve the problem. Two methods for mathematical modeling are focused in detail: Bézier and B-spline. Using these methods a Hodeling System is implemented, giving special atention to the interface aspects of man/machine interation, such as the introduction of the necessary tridiImensional data and the visualisation of the objects projected. This implementation is based on Software Engineering techniques selected for solving this kind of problem
Mestrado
Mestre em Engenharia Elétrica
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Lopes, Raquel Vieira 1983. "Sk-splines de funções periódicas." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306562.
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Orientador: Sérgio Antonio TozoniDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Os sk-splines são uma generalização natural dos splines polinomiais, os quais foram introduzidos e tiveram sua teoria básica desenvolvida por Alexander Kushpel nos anos de 1983-1985. Estas funções são importantes em várias aplicações e seu espaço é gerado por translações discretas de uma única função núcleo. Neste trabalho, estudamos condições necessárias e suficientes para a existência e unicidade de sk-splines interpolantes de funções periódicas. Além disso, estudamos a aproximação de funções de determinadas classes por sk-splines nos espaços Lp. Como aplicação estudamos a aproximação de funções infinitamente diferenciáveis e finitamente diferenciáveis por sk- splines
Abstract: The sk-splines are a natural generalization of polynomial splines. They were introduced and their basic theory developed by Alexander Kushpel between 1983 and 1985. These functions are important in many applications and the space of sk-splines is the linear span of shifts of a single kernel K. In this work, we study necessary and sufficient conditions for the existence and uniqueness of sk-splines interpolants of periodic functions. Furthermore, we study the approximation in several classes of functions by sk-splines in the Lp spaces. As an application we study the approximation of infinitely and finitely differentiable functions by sk-splines
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada
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BENAMAR, ABDESSELAM. "Modelisation des courbes sur les surfaces splines et mise en oeuvre des fonctions box splines." Paris 6, 1994. http://www.theses.fr/1994PA066038.
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A partir de l'expression formelle de la courbe image d'une courbe de bezier, sur une facette de bezier, plusieurs approches de constructions de surfaces ayant une continuite geometriques a l'ordre un sont introduites dans le chapitre un. Des applications a ces dernieres sont donnees dans le chapitre deux. Elles consistent a donner des methodes utilisant en particulier l'algorithme de casteljau, permettant de generer des surfaces ayant des trous delimites par des courbes de bezier par morceaux avec continuite geometrique aux points du contact. Le chapitre trois est consacre a la mise en uvre des fonctions box splines a deux variables dans un environnement de calcul formel
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Benatar, Michael A. "An Experimental Investigation of the Load Distribution of Splined Joints under Gear Loading Conditions." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460908970.
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Andrew, Steven Paul. "Tools for the simulation and analysis of aerodynamic models." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1176224995.
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Huang, Fuping. "Nonparametric censored regression by smoothing splines." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ61977.pdf.
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Zhou, Jingfang. "Interval simplex splines for scientific databases." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/38060.
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Kelil, Abey Sherif. "Bivariate box splines and surface subdivision." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80387.
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Gomide, Anamaria 1949. "Splines polinomiais não homogeneos na esfera." [s.n.], 1999. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260855.
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Orientador: Jorge Stolfi, Marcio Luiz de AndradeTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Estudamos neste trabalho o método de elementos finitos para aproximação de funções, e integração de equações diferenciais parciais sobre a esfera S2. Tais problemas ocorrem em várias aplicações práticas, incluindo modelagem global do tempo, geofísica, iluminação, etc. Definimos um polinômio esférico como sendo a restrição à esfera sn-l de um polinômio nas coordenadas cartesianas (Xl, x2,.", xn) de Rn. Denotamos por pd,n /sn-l o espaço de todos os polinômios esféricos de grau total :s:d, e por 1ld,n/sn-l o espaço dos polinômios esféricos homogêneos de grau total d. As funções que investigamos são as funções esféricas Cr polinomiais por partes, ou splines esféricos Cr, definidos em relação a uma triangulação esférica T de sn-l. Seja p~,n[T]/sn-l o espaço de todas as funções f de sn-l em R tais que (1) a restrição de f a cada triângulo de T coincide com uma função de pd,n/sn-l; e (2) a função f tem continuidade de ordem-r através das fronteiras de T. Analogamente, seja 1l~,n[TJlsn-l o sub-espaço de p~,n[T]/sn-l dos splines esféricos homogêneos, que consiste das funções que são 1ld,n/sn-l em cada triângulo de T. Neste trabalho mostramos que pd,n/sn-l = 1ld-l,n /sn-l EB1ld,n/sn-l, e estendemos esse resultado aos splines esféricos, mostrando que p~,n[TJlsn-l = 1l~-l,n[TJlsn-l EB1l~,n[T]jsn-l. Alfeld, Neamtu e Schumaker propuseram recentemente o espaço 1l~[TJlS2 para aproximação na esfera S2, e obtiveram uma construção explícita de uma base para o espaço 1l~[T]/S2, quando d 2: 3r + 2. Combinando .esta construção com o nosso resultado, acima descrito, nós obtemos uma base local explícita para o espaço P~[T]jS2 quando d 2:3r + 3. Nossa tese é que o P~[T]jS2 é um espaço de aproximação mais natural e eficaz do que 1l~[T]/S2. Analisamos, em particular, o uso dos espaços Pg[T]jS2 e Pf[T]jS2 para aproximar funções restritas a esfera S2, pelo critério dos mínimos quadrados. Analisamos também o uso do espaço Pf[TJlS2 para resolução numérica de equações diferenciais parciais na esfera, pelo método dos elementos finitos, e descrevemos uma técnica multi-escala para acelerar a convergência em malhas finas
Abstract: We study in this work the finite element method for function approximation and integration of partial differential equation on the sphere S2. These problems occur in many pratical applications, including global weather modeling, geophysics, illumination, etc.. A spherical polynomial is the restriction to the sphere sn-l of a polynomial in the coordinates Xl, X2,. . . , Xn of Rn. We denote by pd,n/sn-l the space of spherical polynomials with total degree :::; d, and by 1íd,n/sn-l the space of homogeneous spherical polynomials with total degree d. The functions we investigate are the Cr piecewise polynomial functions on sn-l, or Cr spherical splines, defined relative to a spherical triangulation T on the sphere sn-l. Let p~,n[T]jsn-l be the space of all functions f from sn-l to R such that (1) the restriction of f to each triangle of T matches some function in pd,n /sn-l; and (2) the function f has order-r continuity across the boundaries of T. Analogously, let 1í~,n[T]jsn-1 denote the subspace ofP~,n[T]/sn-l, the homogeneous spherical splines, which consists of the functions that are 1íd,n/sn-l within each triangle of T. We show that pd,n/sn-l = 1íd,n/sn-l EB1íd-l,n /sn-l, and generalize this result to spherical splines, showing that p~,n[T]jsn-1 = 1í~,n[T]jsn-1 EB1í~-I,n[T]jsn-l. Alfeld, Neamtu and Shumaker proposed recently the space 1í~[T]jS2 for approximation on the sphere S2, and they obtained explicit bases for that space, when d 2 3r + 2. Combining their construction with our result above, we obtain explicit local bases for the spaces p~[T]jS2, when d 2 3r + q. We argue that the space P~[T]jS2 is a more natural and effective tool than 1í~[T]jS2 for approximation on the sphere. We analyze, in particular, the use of spaces Pg[T]jS2 and Pf[T]jS2 for least squares function approximation on the sphere S2. We analyze also the use of the space Pf[T]jS2 in the numerical integration of partial differential equations; and we describe a multi-scale technique for accelerating the convergence on large grids
Doutorado
Doutor em Engenharia Elétrica
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Silva, Luiz Marcelo Chiesse da. "Geração de b-splines via FPGA." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18152/tde-10102012-084652/.
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As b-splines são utilizadas em sistemas CAD/CAM/CAE para representar e definir curvas e superfícies complexas, sendo adotada pelos principais padrões da computação gráfica devido a características como representação matemática de forma compacta, flexibilidade e transformações afins. Em sistemas de aquisição de dados 3D e sistemas CAM-CNC integrados, a utilização da b-spline na transferência de informações geométricas e na reconstrução da superfície de objetos resulta em um significativo incremento na eficiência do processo, geralmente implementado em sistemas embarcados. Nestes sistemas embarcados, integrados no auxílio a máquinas de manufatura, a utilização de FPGAs é incipiente, sem circuitos para b-splines disponibilizados em lógica reconfigurável de circuito aberto (open core), razão pela qual este projeto propõe o desenvolvimento de um circuito de geração b-spline aberto, em um sistema embarcado FPGA, utilizando algoritmos adaptados para os circuitos, elaborados em linguagem Verilog HDL, padronizada para a síntese de circuitos em lógica reconfigurável. Os circuitos foram desenvolvidos, utilizando-se um barramento de dados padronizado em circuito aberto, nas seguintes implementações para processamento paralelo das b-splines: o BFEA, o método baseado em funções base fixas, ambos projetados para circuitos integrados, e o fast Cox-de Boor, desenvolvido para FPGAs. Foram comparados o tempo de execução e o consumo de recursos disponíveis no FPGA utilizado, entre cada implementação. Os resultados evidenciaram que os circuitos de funções base fixas apresentaram o processamento mais rápido para a geração de b-splines em um FPGA, com um tempo de execução em média 20% menor em relação às outras implementações. Os circuitos BFEA apresentaram a menor utilização de elementos lógicos, em média 50% menor em relação aos outros circuitos implementados. O circuito fast Cox-de Boor apresentou a melhor escalabilidade, devido à modularidade da implementação, com tempos de execução similares aos circuitos de funções base fixas.The b-splines are used in CAD/CAM/CAE systems to represent and define complex curves and surfaces, being adopted by the main computer graphics standards due to features like compact mathematic representation, flexibility and affine transformations. In 3D acquisition systems and integrated CAM-CNC systems, the use of the b-spline in the geometric information data transfer and in the object surface reconstruction results in a increase in the process efficiency, generally implemented in embedded systems. In these embedded systems, integrated in the aid to manufacturing machines, the use of FPGAs is incipient, without available b-splines open core circuits in reconfigurable logic, the reason why this project propose the development of a b-spline generation open core circuit, in a FPGA embedded system, using adaptated algorithms for the circuits, made in Verilog HDL language, standardized for the circuit synthesis in reconfigurable logic. The circuits were developed, using an open core standardized data bus, in the following implementations of b-spline parallel processing: the BFEA, fixed basis functions based method, both designed for integrated circuits, and the fast Cox-de Boor, developed for FPGAs. The execution time and available resource consumption in the FPGA were compared, between each implementation. The results show that the fixed basis functions circuits presented the fastest processing for the b-splines generation in a FPGA, with a 20% mean execution time reduction in relation to the other implementations. The BFEA circuits presented the lowest logic elements use, in mean 50% fewer in relation to the other implemented circuits. The fast Cox-De Boor circuit presented the best scalability, due to the implementation modularity, with execution times similar to the fixed basis functions circuits.
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Tomek, Peter. "Approximation of Terrain Data Utilizing Splines." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236488.
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Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané terenní data na určitých bodech spolu s gradientem pomocí vícerozměrných splajnů. Program by měl vyčíslit více bodů najednou a měl by pracovat v $n$-dimensionálním prostoru.
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LI, MIN. "TWO ESSAYS IN BAYESIAN PENALIZED SPLINES." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1029342150.
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Miyata, Satoshi. "Adaptive free-knot splines and inference /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486399451962014.
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Zhou, Shanggang. "Regression splines : some theories and algorithms /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487952208107795.
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ZAAMOUN, SAAD. "Fonctions splines en analyse des donnees." Paris, CNAM, 1989. http://www.theses.fr/1989CNAM0100.
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L'etude qu'on presente porte sur l'analyse non lineaire de donnees. Ce type d'analyse etait jusqu'a recemment aborde de facon assez simple en transformant les variables a l'aide de fonctions indicatrices; ce qui necessite des decoupages en classes des valeurs prises par les variables et ne permet pas de tenir compte du comportement de celles-ci a l'interieur des classes. Pour remedier a ce defaut, on propose l'utilisation de fonctions splines dont le choix est renforce par leur stabilite numerique et la facilite des calculs qu'elles engendrent. Le chapitre i comporte un resume des resultats de m. Duc jacquet utilises dans la suite de la these. Le chapitre ii est consacre a l'analyse en composantes principales non lineaires avec fonctions splines. L'a. C. P. Lineaire classique apparait alors comme un cas particulier correspondant au degre zero. La formule d'inertie est aussi generalisee dans ce cadre. Le chapitre iii traite de l'a. C. P. En dimension infinie. Le recours aux espaces de sobolev vient alors naturellement. Une application de cette methode concerne l'etude du calendrier de constitution des familles (j. C. Deville) comme exemple de donnees temporelles. Le chapitre iv est relatif a la regression non lineaire et une generalisation des regressions simple et multiple est proposee. Le chapitre v concerne l'analyse canonique avec fonctions splines et l'on generalise encore la formule d'inertie expliquee par les facteurs. L'analyse des correspondances multiples lineaire classique apparait alors comme un cas particulier correspondant au degre zero des splines utilisees. Enfin au chapitre vi, on fait l'extension de l'analyse en composantes principales de variables instrumentales a l'aide de fonctions splines
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Hassan, Mosavverul Meir Amnon J. "Constructing cubic splines on the sphere." Auburn, Ala., 2009. http://hdl.handle.net/10415/1790.
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Ferreira, de Oliveira Eric. "Reconstrução Tomográfica com superfícies B-splines." Universidade Federal de Pernambuco, 2011. https://repositorio.ufpe.br/handle/123456789/9445.
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Previous issue date: 2011Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Vários estudos têm indicado que, das várias classes de algoritmos de reconstrução aplicáveis para dados limitados, os baseados na técnica de reconstrução algébrica são mais flexíveis e precisos. Infelizmente, estas técnicas, geralmente, sofrem de ruídos ocasionados por processos de correção durante a reconstrução e também por inconsistências nos dados adquiridos pelos tomógrafos. O pós - processamento da imagem reconstruída com a aplicação de filtros pode ser feito para atenuar a presença de ruídos, mas geralmente atenuam também as descontinuidades presentes em bordas que distinguem objetos ou falhas. O presente trabalho propõe a redução de ruídos assegurando a continuidade (das derivadas) da superfície antes da reconstrução, representando cada incógnita por uma combinação linear de pontos de controle e suas bases B-splines. São aplicadas três bases Bsplines: B1 , B2 e B3, assegurando as continuidade C0, C1 e C2, respectivamente. Para validação da técnica, foram utilizadas simulações de modelos propostos na literatura e medidas experimentais por tomografia gama. Os resultados foram comparados com as técnicas algébricas ART, SIRT, MART e SMART, sendo validada satisfatoriamente para todos os phantoms propostos. Todas as bases B-splines aplicadas obtiveram erros menores que as técnicas de correção ART e SIRT, sendo a B3, a de melhor desempenho. Este resultado pode ser explicado pelas restrições de suavidade impostas à superfície reconstruída pelas bases Bsplines e a inclinação das técnicas aditivas a ruídos, principalmente para um número limitado de dados (5 e 10 vistas). A performance das técnicas multiplicativas para essa situação é a melhor, mostrando uma imagem sem artefatos e com pouco ruído. Devido a esse fato, a técnica b-spline não tem bons resultados, apresentando na maioria dos casos, erros maiores. Para todos os testes realizados, as técnicas de representação B-splines superaram os filtros de mesma natureza aplicados no pós-processamento, sugerindo que a técnica seja utilizada no lugar da filtragem pós-processamento
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Alibert, Jean-Jacques. "Variétés splines en élasticité non linéaire." Toulouse 3, 1990. http://www.theses.fr/1990TOU30142.
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On etablit l'existence d'un champ de deplacement defini sur un ouvert de r#3, satisfaisant des conditions d'interpolation par moyennes locales ou bien une condition d'incompressibilite, et minimisant l'energie totale de deformation d'un materiau de saint-veant-kirchhoff. La condition d'incompressibilite est envisagee dans le cas ou est une partie bornee de r#s3 tandis que dans le cas ou est l'espace r#3 tout entier, est pris en compte un nombre infini de conditions d'interpolation. Dans toutes les situations etudiees, la solution du probleme d'optimisation satisfait les equations d'equilibre correspondantes et reciproquement
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Henriksen, Ian Daniel. "Evaluation and Refinement of Generalized B-splines." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5887.
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In this thesis a method for direct evaluation of Generalized B-splines (GB-splines) via the representation of these curves as piecewise functions is presented. A local structure is introduced that makes the GB-spline curves more amenable to the integration used in constructing bases of higher degree. This basis is used to perform direct computation of piecewise representation of GB-spline bases and curves. Algorithms for refinement using these local structures are also developed.
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Tazeroualti, Mohammed. "Modélisation de surfaces à l'aide de fonctions splines : conception d'un verre progressif." Grenoble 1, 1993. http://tel.archives-ouvertes.fr/tel-00343495.
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Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide
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Kriner, Monika. "Survival Analysis with Multivariate adaptive Regression Splines." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-73695.
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Xiang, Hong. "Cardinal interpolation by splines and refinable functions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq39609.pdf.
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Mössner, Bernhard [Verfasser]. "B-Splines als Finite Elemente / Bernhard Mössner." Aachen : Shaker, 2006. http://d-nb.info/1186582669/34.
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Polyak, Ilya. "Estimating the know locations of noisy splines." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/36986.
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Morellato, Saulo Almeida 1983. "Inferência estatística para regressão múltipla h-splines." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306505.
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Orientador: Ronaldo DiasTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Este trabalho aborda dois problemas de inferência relacionados à regressão múltipla não paramétrica: a estimação em modelos aditivos usando um método não paramétrico e o teste de hipóteses para igualdade de curvas ajustadas a partir do modelo. Na etapa de estimação é construída uma generalização dos métodos h-splines, tanto no contexto sequencial adaptativo proposto por Dias (1999), quanto no contexto bayesiano proposto por Dias e Gamerman (2002). Os métodos h-splines fornecem uma escolha automática do número de bases utilizada na estimação do modelo. Estudos de simulação mostram que os resultados obtidos pelos métodos de estimação propostos são superiores aos conseguidos nos pacotes gamlss, mgcv e DPpackage em R. São criados dois testes de hipóteses para testar H0 : f = f0. Um teste de hipóteses que tem sua regra de decisão baseada na distância quadrática integrada entre duas curvas, referente à abordagem sequencial adaptativa, e outro baseado na medida de evidência bayesiana proposta por Pereira e Stern (1999). No teste de hipóteses bayesiano o desempenho da medida de evidência é observado em vários cenários de simulação. A medida proposta apresentou um comportamento que condiz com uma medida de evidência favorável à hipótese H0. No teste baseado na distância entre curvas, o poder do teste foi estimado em diversos cenários usando simulações e os resultados são satisfatórios. Os procedimentos propostos de estimação e teste de hipóteses são aplicados a um conjunto de dados referente ao trabalho de Tanaka e Nishii (2009) sobre o desmatamento no leste da Ásia. O objetivo é escolher um entre oito modelos candidatos. Os testes concordaram apontando um par de modelos como sendo os mais adequados
Abstract: In this work we discuss two inference problems related to multiple nonparametric regression: estimation in additive models using a nonparametric method and hypotheses testing for equality of curves, also considering additive models. In the estimation step, it is constructed a generalization of the h-splines method, both in the sequential adaptive context proposed by Dias (1999), and in the Bayesian context proposed by Dias and Gamerman (2002). The h-splines methods provide an automatic choice of the number of bases used in the estimation of the model. Simulation studies show that the results obtained by proposed estimation methods are superior to those achieved in the packages gamlss, mgcv and DPpackage in R. Two hypotheses testing are created to test H0 : f = f0. A hypotheses test that has a decision rule based on the integrated squared distance between two curves, for adaptive sequential approach, and another based on the Bayesian evidence measure proposed by Pereira and Stern (1999). In Bayesian hypothesis testing the performance measure of evidence is observed in several simulation scenarios. The proposed measure showed a behavior that is consistent with evidence favorable to H0. In the test based on the distance between the curves, the power of the test was estimated at various scenarios using simulations, and the results are satisfactory. At the end of the work the proposed procedures of estimation and hypotheses testing are applied in a dataset concerning to the work of Tanaka and Nishii (2009) about the deforestation in East Asia. The objective is to choose one amongst eight models. The tests point to a pair of models as being the most suitableIn this work we discuss two inference problems related to multiple nonparametric regression: estimation in additive models using a nonparametric method and hypotheses testing for equality of curves, also considering additive models. In the estimation step, it is constructed a generalization of the h-splines method, both in the sequential adaptive context proposed by Dias (1999), and in the Bayesian context proposed by Dias and Gamerman (2002). The h-splines methods provide an automatic choice of the number of bases used in the estimation of the model. Simulation studies show that the results obtained by proposed estimation methods are superior to those achieved in the packages gamlss, mgcv and DPpackage in R. Two hypotheses testing are created to test H0 : f = f0. A hypotheses test that has a decision rule based on the integrated squared distance between two curves, for adaptive sequential approach, and another based on the Bayesian evidence measure proposed by Pereira and Stern (1999). In Bayesian hypothesis testing the performance measure of evidence is observed in several simulation scenarios. The proposed measure showed a behavior that is consistent with evidence favorable to H0. In the test based on the distance between the curves, the power of the test was estimated at various scenarios using simulations, and the results are satisfactory. At the end of the work the proposed procedures of estimation and hypotheses testing are applied in a dataset concerning to the work of Tanaka and Nishii (2009) about the deforestation in East Asia. The objective is to choose one amongst eight models. The tests point to a pair of models as being the most suitable
Doutorado
Estatistica
Doutor em Estatística
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Flores, Flores Claudio Jaime. "Modelo de regresión de Cox usando splines." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2011. https://hdl.handle.net/20.500.12672/211.
Full textAbstract:
En muchos estudios clínicos es muy frecuente el uso de modelo de riesgos proporcionales de Cox; el cual asume riesgos proporcionales y restringe a que el logaritmo de la razón de riesgo sea lineal en las covariables, lo cual en muchos casos no se verifica. En este sentido, una forma funcional no lineal del efecto de las covariables puede ser aproximada por una función spline. En este trabajo, se presenta la metodología del modelo de regresión de Cox usando splines, particularmente regresión splines y P-splines, para aproximar la forma funcional no-lineal de los efectos de las covariables en la función de riesgo. Como una aplicación, se analiza los datos de pacientes con LNH para determinar los factores pronósticos para la supervivencia global. Los resultados muestran que el efecto de las covariables contínuas como hemoglobina, leucocitos, linfocitos y DHL presentan una forma funcional no lineal en el logaritmo de la razón de riesgo.
-- Palabras claves: Modelo de Cox, regresión splines, P-splines, LNH.-- In many clinical studies, Cox proportional hazard model is very common to use, it assumes proportional hazard and restricts the log hazard ratio to be linear in the covariates; these asumptions can not be verified. In this way, a nonlinear functional form of the covariates effect can be approximated by a spline function. In this paper, we present the methodology and an application of Cox model using splines, particularly regression splines and P-splines, to approximate the nonlinear functional form of the effect of covariates on the hazard function. As an application, we analyse data from patients with NHL to determine prognostic factors for overall survival. These results show that the effect of continuous covariates as: hemoglobin, leukocytes, lymphocytes and LDH have a nonlinear form with the log hazard ratio. -- Keywords: Cox model, regression splines, P-spline, NHL.
Tesis
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Park, Jae H. "Chebyshev Approximation of Discrete polynomials and Splines." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/30195.
Full textAbstract:
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 many applications, Chebyshev approximation with polynomials and splines is useful in representing a stream of data or a function. Because the impulse/summation approach is developed for discrete systems, some aspects of traditional continuous approximation are not applicable. For example, the lack of the continuity concept in the discrete domain affects the definition of the local extrema of a function. Thus, the method of finding the extrema must be changed. Both forward differences and backward differences must be checked to find extrema instead of using the first derivative in the continuous domain approximation. Polynomial Chebyshev approximation in the discrete domain, just as in the continuous domain, forms a Chebyshev system. Therefore, the Chebyshev approximation process always produces a unique best approximation. Because of the non-linearity of free knot polynomial spline systems, there may be more than one best solution and the convexity of the solution space cannot be guaranteed. Thus, a Remez Exchange Algorithm may not produce an optimal approximation. However, we show that the discrete polynomial splines approximate a function using a smaller number of parameters (for a similar minimax error) than the discrete polynomials do. Also, the discrete polynomial spline requires much less computation and hardware than the discrete polynomial for curve generation when we use the impulse/summation approach. This is demonstrated using two approximated FIR filter implementations.Ph. D.
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May, Stefan. "Splines for damage and fracture in solids." Thesis, University of Glasgow, 2016. http://theses.gla.ac.uk/7284/.
Full textAbstract:
This thesis addresses different aspects of numerical fracture mechanics and spline technology for analysis. An energy-based arc-length control for physically non-linear problems is proposed. It switches between an internal energy-based and a dissipation-based arc-length method. The arc-length control allows to trace an equilibrium path with multiple snap-through and/or snap-back phenomena and only requires two parameters. Phase field models for brittle and cohesive fracture are numerically assessed. The impact of different parameters and boundary conditions on the phase field model for brittle fracture is investigated. It is demonstrated that Γ-convergence is not attained numerically for the phase field model for brittle fracture and that the phase field model for cohesive fracture does not pass a two-dimensional patch test when using an unstructured mesh. The properties of the Bézier extraction operator for T-splines are exploited for the determination of linear dependencies, partition of unity properties, nesting behaviour and local refinement. Unstructured T-spline meshes with extraordinary points are modified such that the blending functions fulfil the partition of unity property and possess a higher continuity. Bézier extraction for Powell-Sabin B-splines is introduced. Different spline technologies are compared when solving Kirchhoff-Love plate theory on a disc with simply supported and clamped boundary conditions. Powell-Sabin B-splines are utilised for smeared and discrete approaches to fracture. Due to the higher continuity of Powell-Sabin B-splines, the implicit fourth order gradient damage model for quasi-brittle materials can be solved and stresses can be computed directly at the crack tip when considering the cohesive zone method.
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Li, Wan-Chiu Paul Jean-Claude. "Conversion automatique de maillages en surfaces splines." S. l. : INPL, 2006.
Find full text
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Li, Jingang. "Isogeometric Finite Element Analysis Using T-Splines." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd3159.pdf.
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Flores, Flores Claudio Jaime, and Flores Claudio Jaime Flores. "Modelo de regresión de Cox usando splines." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2011. http://cybertesis.unmsm.edu.pe/handle/cybertesis/211.
Full textAbstract:
En muchos estudios clínicos es muy frecuente el uso de modelo de riesgos proporcionales de Cox; el cual asume riesgos proporcionales y restringe a que el logaritmo de la razón de riesgo sea lineal en las covariables, lo cual en muchos casos no se verifica. En este sentido, una forma funcional no lineal del efecto de las covariables puede ser aproximada por una función spline. En este trabajo, se presenta la metodología del modelo de regresión de Cox usando splines, particularmente regresión splines y P-splines, para aproximar la forma funcional no-lineal de los efectos de las covariables en la función de riesgo. Como una aplicación, se analiza los datos de pacientes con LNH para determinar los factores pronósticos para la supervivencia global. Los resultados muestran que el efecto de las covariables contínuas como hemoglobina, leucocitos, linfocitos y DHL presentan una forma funcional no lineal en el logaritmo de la razón de riesgo.
-- Palabras claves: Modelo de Cox, regresión splines, P-splines, LNH.-- In many clinical studies, Cox proportional hazard model is very common to use, it assumes proportional hazard and restricts the log hazard ratio to be linear in the covariates; these asumptions can not be verified. In this way, a nonlinear functional form of the covariates effect can be approximated by a spline function. In this paper, we present the methodology and an application of Cox model using splines, particularly regression splines and P-splines, to approximate the nonlinear functional form of the effect of covariates on the hazard function. As an application, we analyse data from patients with NHL to determine prognostic factors for overall survival. These results show that the effect of continuous covariates as: hemoglobin, leukocytes, lymphocytes and LDH have a nonlinear form with the log hazard ratio. -- Keywords: Cox model, regression splines, P-spline, NHL.
Tesis
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Li, Wan-Chiu. "Conversion automatique de maillages en surfaces splines." Thesis, Vandoeuvre-les-Nancy, INPL, 2006. http://www.theses.fr/2006INPL078N/document.
Full textAbstract:
Afin de convertir un maillage triangulaire en une surface spline de CAGD/CAM, cette thèse adresse l’un des problèmes les plus cruciaux du processus de conversion : extraire un “bon” maillage de contrôle quadrilatéral de la surface. Ce que nous entendons par “bon” est que les arêtes du maillage de contrôle se croisent perpendiculairement et sont alignées avec les principales directions de la courbure de la surface. Ces deux propriétés du maillage de contrôle permettent de fournir une bonne approximation de la surface avec peu de points de contrôles. D’ailleurs, ils aident considérablement à réduire des oscillations non désirées sur la surface spline finale. Pour résoudre ce problème, nous proposons un nouvel algorithme automatique, appelé paramétrisation globale périodique. L’idée fondamentale de cet algorithme est de trouver une paramétrisation qui ait un “sens d’un point de vue géométrique”, pour ce faire, elle doit être guidée par la courbure de la surface, représentée par une paire de champs de direction orthogonaux. Les iso-lignes de cette paramétrisation sont ensuite extraites pour définir un maillage de contrôle qui ait les propriétés requises. Ce maillage de contrôle, nous permet de construire une approximation en surface T-spline de la surface triangulée initiale. Nous exposons plusieurs résultats de cette conversion d’un maillage triangulée en surface spline. Les résultats montrent que, grâce aux maillages de contrôle anisotropes, les surfaces spline finales ont beaucoup moins d’oscillations que celles construites par les méthodes précédentes qui ne tiennent pas compte de l’anisotropie de la surfaceAiming at converting a triangular mesh into a CAGD/CAM spline surface, this thesis focuses on one of the most crucial problems of the conversion process, i.e. extracting a “good” quadrilateral control mesh of the surface. What we mean by good is that the edges of the control mesh should be orthogonal and aligned with the principal directions of curvature of the surface. These two properties make the control mesh optimum in an approximation point of view, and greatly help to reduce unwanted oscillations on the final spline surface built from it. To solve this problem, we propose a new automatic algorithm, called periodic global parameterization. The basic idea is to find a “geometry-meaningful” parameterization guided by a pair of orthogonal anisotropic direction fields. Then, the iso-value lines of this parameterization will be extracted to define an initial control mesh, that satisfies the two criteria of a good control mesh. With the initial control mesh, we explain how to construct a T-spline approximation of the initial triangulated surface. We show several examples of the triangular mesh to T-spline conversion. The results show that thanks to the anisotropic control meshes, the final spline surfaces generated have much less oscillations as compared to results of previous methods, that do not take into account of the anisotropy
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Li, Wan-Chiu. "Conversion automatique de maillages en surfaces splines." Electronic Thesis or Diss., Vandoeuvre-les-Nancy, INPL, 2006. http://www.theses.fr/2006INPL078N.
Full textAbstract:
Afin de convertir un maillage triangulaire en une surface spline de CAGD/CAM, cette thèse adresse l’un des problèmes les plus cruciaux du processus de conversion : extraire un “bon” maillage de contrôle quadrilatéral de la surface. Ce que nous entendons par “bon” est que les arêtes du maillage de contrôle se croisent perpendiculairement et sont alignées avec les principales directions de la courbure de la surface. Ces deux propriétés du maillage de contrôle permettent de fournir une bonne approximation de la surface avec peu de points de contrôles. D’ailleurs, ils aident considérablement à réduire des oscillations non désirées sur la surface spline finale. Pour résoudre ce problème, nous proposons un nouvel algorithme automatique, appelé paramétrisation globale périodique. L’idée fondamentale de cet algorithme est de trouver une paramétrisation qui ait un “sens d’un point de vue géométrique”, pour ce faire, elle doit être guidée par la courbure de la surface, représentée par une paire de champs de direction orthogonaux. Les iso-lignes de cette paramétrisation sont ensuite extraites pour définir un maillage de contrôle qui ait les propriétés requises. Ce maillage de contrôle, nous permet de construire une approximation en surface T-spline de la surface triangulée initiale. Nous exposons plusieurs résultats de cette conversion d’un maillage triangulée en surface spline. Les résultats montrent que, grâce aux maillages de contrôle anisotropes, les surfaces spline finales ont beaucoup moins d’oscillations que celles construites par les méthodes précédentes qui ne tiennent pas compte de l’anisotropie de la surfaceAiming at converting a triangular mesh into a CAGD/CAM spline surface, this thesis focuses on one of the most crucial problems of the conversion process, i.e. extracting a “good” quadrilateral control mesh of the surface. What we mean by good is that the edges of the control mesh should be orthogonal and aligned with the principal directions of curvature of the surface. These two properties make the control mesh optimum in an approximation point of view, and greatly help to reduce unwanted oscillations on the final spline surface built from it. To solve this problem, we propose a new automatic algorithm, called periodic global parameterization. The basic idea is to find a “geometry-meaningful” parameterization guided by a pair of orthogonal anisotropic direction fields. Then, the iso-value lines of this parameterization will be extracted to define an initial control mesh, that satisfies the two criteria of a good control mesh. With the initial control mesh, we explain how to construct a T-spline approximation of the initial triangulated surface. We show several examples of the triangular mesh to T-spline conversion. The results show that thanks to the anisotropic control meshes, the final spline surfaces generated have much less oscillations as compared to results of previous methods, that do not take into account of the anisotropy
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Robins, Robert R. "Tooth Engagement Evaluation of Involute Spline Couplings." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2605.pdf.
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Mendoza, Natalie Veronika Rondinel. "Estruturas unidimensionais e bidimensionais utilizando P-splines nos modelos mistos aditivos generalizados com aplicação na produção de cana-de-açúcar." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-22032018-145655/.
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Os P-splines de Eilers e Marx (1996) são métodos de suavização que é uma combinação de bases B-splines e uma penalização discreta sobre os coeficientes das bases utilizados para suavizar dados normais e não normais em uma ou mais dimensões, no caso de várias dimensões utiliza-se como suavização o produto tensor dos P-splines. Também os P-splines são utilizados como representação de modelos mistos Currie et al. (2006) pela presença de características tais como: efeitos fixos, efeitos aleatórios, correlação espacial ou temporal e utilizados em modelos mais generalizados tais como os modelos mistos lineares generalizados e modelos mistos aditivos generalizados. Neste trabalho apresentou-se toda a abordagem, metodologia e descrição dos P-splines como modelos mistos e como componentes das estruturas suavizadoras de variáveis unidimensionais e bidimensionais dos modelos mistos aditivos generalizados, mostrando essa abordagem e propondo seu uso em uma aplicação no comportamento dos níveis médios da produção de cana-de-açúcar sob a influência das alterações das variáveis climáticas como temperatura e precipitação, que foram medidos ao longo de 10 anos em cada mesorregião do Estado de São Paulo. O motivo de usar essa abordagem como método de suavização é que muitas vezes não é conhecido a tendência dessas covariáveis climáticas mas sabe-se que elas influenciam diretamente sobre a variável resposta. Além de permitir essa abordagem inclusão de efeitos fixos e aleatórios nos modelos a serem propostos, permitirá a inclusão do processo autoregressivo AR(1) como estrutura de correlação nos resíduos.P-splines of Eilers e Marx (1996) are methods of smoothing that is a combination of B-splines bases and penalty the coefficients of the bases used to smooth normal and non-normal data in one or more dimensions; in the case of several dimensions it is used as smoothing the tensor product of the P-splines. Also the P-splines are used as representation of mixed models Currie et al. (2006) by the presence of characteristics such as: fixed effects, random effects, spatial or temporal correlation and used in more generalized models such as generalized linear mixed models and generalized additive mixed models. In this work the whole approach, methodology and description of the P-splines as mixed models and as components of the smoothing structures of one-dimensional and two-dimensional variables of generalized additive mixed models were presented, showing this approach and proposing its application in the behavior of the average levels of sugarcane production, which is influenced by changes in climatic variables such as temperature and precipitation , which were measured over 10 years in each mesoregion of the state of São Paulo. The reason for using this approach as a smoothing method is that the tendency of these climate covariables is not know for the most part, but is known that they influence directly the response variable, besides allowing this approach to include fixed and random effects in the models to be proposed, will allow the inclusion of the autoregressive process AR(1) as a correlation structure in the residuos.
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Coe, David H. "Skinning engineering models with non-uniform, hierarchical B-spline surfaces." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040656/.
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Brezger, Andreas. "Bayesian P-Splines in Structured Additive Regression Models." Diss., lmu, 2005. http://nbn-resolving.de/urn:nbn:de:bvb:19-39420.
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Hellton, Kristoffer Herland. "Stochastic Models for Smoothing Splines : A Bayesian Approach." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13724.
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Flexible data regression is an important tool for capturing complicated trends in data. One approach is penalized smoothing splines, where there are several mainstream methods. A weakness is, however, the quantification of uncertainty. We will in thesis present two mainstream smoothing spline methods, P-splines and O'Sullivan splines, and the RW2 model; a Bayesian hierarchical model based on a latent field. The Bayesian priors are specified by a stochastic Poisson equation, and spline estimates are approximated along a finite element Galerkin approach. We evaluate the three methods using integrated nested Laplace approximations (INLA) for a full Bayesian analysis supplying credible bands. The methods give fairly similar results and we investigate the theoretical motivates behind the methods. As an extension of the Bayesian models, the smoothing parameter is incorporated in latent field. This gives an adaptive smoothing method, which better estimates jumps and quick curvature changes. Further, the close relationship between O'Sullivan splines smoothing splines is discussed, revealing O'Sullivan splines to be a finite element Petrov-Galerkin approximation of smoothing splines. The main results are the possibility of credible bands, the extension to adaptive smoothing and the finite element understanding of O'Sullivan splines.