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Dissertations / Theses on the topic 'Linear dependence (Mathematics)'
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Seater, Robert. "Efficient handling of dependence analysis for arrays." Diss., Connect to the thesis, 2002. http://hdl.handle.net/10066/1541.
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Ma, Jinhua. "Dependency modeling for information fusion with applications in visual recognition." HKBU Institutional Repository, 2013. https://repository.hkbu.edu.hk/etd_ra/1522.
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Petersson, Niclas. "The Maximum Displacement for Linear Probing Hashing." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9545.
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In this thesis we study the standard probabilistic model for hashing with linear probing. The main purpose is to determine the asymptotic distribution for the maximum displacement. Depending on the ratio between the number of items and the number of cells, there are several cases to consider. Paper I solves the problem for the special case of almost full hash tables. That is, hash tables where every cell but one is occupied. Paper II completes the analysis by solving the problem for all remaining cases. That is, for every case where the number of items divided by the number of cells lies in the interval [0,1]. The last two papers treat quite different topics. Paper III studies the area covered by the supremum process of Brownian motion. One of the main theorems in Paper I is expressed in terms of the Laplace transform of this area. Paper IV provides a new sufficient condition for a collection of independent random variables to be negatively associated when conditioned on their total sum. The condition applies to a collection of independent Borel-distributed random variables, which made it possible to prove a Poisson approximation that where essential for the completion of Paper II.
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Bružaitė, Kristina. "Some linear models of time series with nonstationary long memory." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20090312_091000-74094.
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In the thesis is studied the limit distribution of partial sums of certain linear time series models with nonstationary long memory and certain statistics which involve partial sums processes.
Philippe, Surgailis, Viano (2006, 2008) introduced time-varying fractionally integrated filters and studied the limit distribution of partial sums processes of these filters under finite variance set-up. In the thesis is studied the limit distribution of partial sums processes of infinite variance time-varying fractionally integrated filters. We assume that the innovations belong to the domain of attraction of an α-stable law (1<α<2) and show that the partial sums process converges to some α-stable self-similar process.
In the thesis is studied the limit of the Increment Ratio (IR) statistic for Gaussian observations superimposed on a slowly varying deterministic trend. The IR statistic was introduced in Surgailis, Teyssière, Vaičiulis (2008) and its limit distribution was studied under the assumption of stationarity of observations. The IR statistic can be used for testing nonparametric hypotheses about d-integrated (-1/2 < d <3/2) behavior of the time series, which can be confused with deterministic trends and change-points. This statistic is written in terms of partial sums process and its limit is closely related to the limit of partial sums. In particularly, the consistency of the IR statistic uses asymptotic independence of distant partial sums, the fact is established in the... [to full text]<br>Disertacijoje ištirti trupmeniškai integruotų tiesinių laiko eilučių modelių su nestacionaria ilgąja atmintimi dalinių sumų ribiniai skirstiniai ir tam tikros statistikos, susijusios su dalinių sumų procesais. Philippe, Surgailis, Viano 2006 ir 2008 m. darbuose apibrėžė kintančius laike trupmeniškai integruotus filtrus su baigtine dispersija ir nagrinėjo jų dalinių sumų ribinius skirstinius. Disertacijoje ištirti tokių procesų dalinių sumų ribiniai skirstiniai, kai dispersija begalinė, laikant, kad inovacijos priklauso α–stabilaus dėsnio traukos sričiai (čia 1<α<2). Įrodyta, kad dalinių sumų procesas konverguoja į tam tikrą α–stabilų savastingąjį procesą su nestacionariais pokyčiais. Surgailis, Teyssière, Vaičiulis 2008 m. darbe įvedė pokyčių santykių arba IR (= Increment Ratio) statistiką ir parodė, kad IR statistika gali būti naudojama tikrinti neparametrinėms hipotezėms apie stacionariosios laiko eilutės ilgąją atmintį bei ilgosios atminties parametrą d. Disertacijoje apibendrinti šių autorių gauti rezultatai, t. y. įrodyta IR statistikos centrinė ribinė teorema ir gauti poslinkio įverčiai, kai stebiniai aprašomi tiesiniu laiko eilutės modeliu su trendu. Praplėsta laiko eilučių klasė, kuriai IR statistika yra pagrįsta, t. y. konverguoja į vidurkį.
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Ramnarayan, Kalind. "Level Dependence in Volatility in Linear-Rational Term Structure Models." Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31207.
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The degree of level dependence in interest rate volatility is analysed in the linearrational term structure model. The linear-rational square-root (LRSQ) model, where level dependence is set a priori, is compared to a specification where the factor process follows CEV-type dynamics which allows a more flexible degree of level dependence. Parameters are estimated using an unscented Kalman filter in conjunction with quasi-maximum likelihood. An extended specification for the state price density process is required to ensure reliable parameter estimates. The empirical analysis indicates that the LRSQ model generally overestimates level dependence. Although the CEV specification captures the degree of level dependence in volatility more accurately, it has a trade-off with analytical tractability. The optimal specification, therefore, depends on the type of model implementation and general economic conditions.
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Schwellnus, Adrian. "Linear-Rational Term Structure Models With Flexible Level-Dependent Volatility." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29215.
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The Linear-Rational Framework for the modelling of interest rates is a framework which allows for the addition of spanned and unspanned factors, while maintaining a lower bound on rates and tractable valuation of interest rate derivatives, particularly swaptions. The advantages of having all these properties are significant. This dissertation presents the Linear-Rational Framework, and specializes the factor process to a class of diffusion models which allows for the degree of state dependence of volatility to be estimated. This dissertation then finds that the estimated state dependent volatility structure is significantly different to that of typical models, where it is set it a priori. The effect the added degree of freedom has on the model implied swaption skew is then analysed.
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Ingram, Mary Ann. "Estimation for linear systems driven by point processes with state dependent rates." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/14887.
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Schuverdt, Maria Laura. "Metodos de lagrangiano aumentado com convergencia utilizando a condição de dependencia linear positiva constante." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307475.
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Orientadores: Jose Mario Martinez, Roberto Andreani<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-05T13:39:47Z (GMT). No. of bitstreams: 1
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Previous issue date: 2006<br>Resumo: Condições de qualificação são ferramentas úteis na análise de convergência de métodos de otimização. Neste trabalho provamos que a nova condição de dependência linear positiva constante (CPLD) é uma condição de qualificação e mostramos que ela é mais fraca que condições clássicas, como regularidade, Mangasarian- Fromovitz e posto constante. Além disso, apresentamos um algo ritmo de Lagrangiano aumentado para resolver problemas gerais de programação matemática com convergência utilizando a CPLD. O algo ritmo proposto é definido para resolver problemas com dois conjuntos de restrições: um, mais complexo, formado pelas restrições que são penalizadas e, outro, mais simples, pelas restrições que são satisfeitas por todos os iterados gerados no processo. O resultado de convergência global estabelece que se um ponto limite da seqüência gerada pelo algoritmo satisfaz a condição CPLD então esse ponto é um ponto estacionário do problema original. O resultado de convergência global obtido é mais forte que resultados de convergência para problemas mais específicos obtidos utilizando condições de qualificação mais fortes, como a regularidade. Indicamos também as hipóteses adequadas sob as quais obtemos limitação do parâmetro de penalidade. A confiabilidade do algo ritmo foi testada mediante uma exaustiva comparação com o algoritmo LANCELOT, mostrando que nosso método é mais robusto e eficiente. Além disso, e como aplicação do nosso algoritmo no caso em que restrições diferentes são incorporadas no problema, apresentamos a resolução de problemas de alocação nos quais existem muitas restrições não-lineares no conjunto complexo. Utilizando o método de Gradiente Projetado Espectral mostramos que problemas desse tipo com muitas variáveis e restrições são resolvidos de maneira eficiente num tempo razoável<br>Abstract: Contraint qualifications are useful tools in the convergence analysis of optimization methods. In this work we prove that the new constant positive linear dependence condition (CPLD) is a constraint qualification and we show that it is weaker than classic constraint qualifications, like the regularity, the Mangasarian-Fromovitz and the constant rank conditions. Moreover, we introduce an augmented Lagrangian algorithm for solving general nonlinear programming problems whose convergence result uses the CPLD condition. The proposed algorithm is developed for problems with two sets of constraints: a complex one, formed by the penalized constraints and a simple one, formed by the constraints that are verified for all the iterates generated along the process. The global convergence result establishes that if a limit point of the sequence generated by the algorithm satisfies the CPLD condition then this point is a stationary point of the original problem. Thus, the global convergence result is stronger than the previous results for more specific problems obtained using stronger constraint qualification, as the regularity. We also indicate suitable conditions under which we prove boundedness of the penalty parameter. The reliability of the approach was tested by means of an exhaustive comparison against LANCELOT, demonstrating that our method is more robust and efficient. Moreover, as an application of our algorithm when different constraints are incorporated, we introduce the resolution of Location Problems in which there exist many nonlinear constraints in the complex set. We show that, employing the Spectral Projected Gradient method for solving the subproblems, this class of problems with many variables and constraints is efficiently solved with moderate computational effort<br>Doutorado<br>Otimização<br>Doutor em Matemática Aplicada
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Bui, Tang Bao Ngoc [Verfasser], Micheal [Akademischer Betreuer] Reissig, Micheal [Gutachter] Reissig, and Karen [Gutachter] Yagdjian. "Semi-linear waves with time-dependent speed and dissipation / Tang Bao Ngoc Bui ; Gutachter: Micheal Reissig, Karen Yagdjian ; Betreuer: Micheal Reissig." Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://d-nb.info/1220911879/34.
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Moreira, Heber Rocha. "Realimentação de saida robusta a partir de controladores dependentes de parametros para sistemas lineares incertos discretos no tempo." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259735.
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Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de Oliveira<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-14T06:55:42Z (GMT). No. of bitstreams: 1
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Previous issue date: 2009<br>Resumo: Esta dissertação trata de um dos mais importantes problemas em aberto na teoria de controle, o projeto de controladores por realimentação estática de saída. A principal contribuição é propor um método para computar controladores robustos estáticos por realimentação de saída para sistemas lineares incertos discretos no tempo, usando um controlador por realimentação de estados como parâmetro de entrada do método. Além disso, os resultados são estendidos para tratar do projeto de controle H2 robusto por realimentação de saída. As condições de síntese são formuladas em termos de um procedimento convexo de otimização, baseado em um conjunto finito de desigualdades matriciais lineares. Exemplos numéricos são apresentados para ilustrar a eficiência dos metodos propostos quando comparados com outros métodos existentes na literatura.<br>Abstract: This thesis deals with one of the most important open problems in control theory, the design of static output feedback controllers. The main contribution is to propose a method to compute robust static output feedback controllers for uncertain linear discrete-time systems, using a state feedback controller as an input parameter for the method. Additionally, the results are extended to cope with H2 static output feedback control design. The synthesis conditions are formulated in terms of a convex optimization procedure, based on a finite set of linear matrix inequalities. Numerical examples are presented to illustrate the effectiveness of the proposed approach compared to other methods available in the literature.<br>Mestrado<br>Automação<br>Mestre em Engenharia Elétrica
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Castillo, René Erlin. "Generalized Non-Autonomous Kato Classes and Nonlinear Bessel Potentials." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1121964346.
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Leite, Valter Junior de Souza. "Estudos sobre estabilidade robusta de sistemas lineares por meio de funções dependentes de parametros." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260564.
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Orientador: Pedro Luis Dias Peres<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-05T03:23:54Z (GMT). No. of bitstreams: 1
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Previous issue date: 2005<br>Resumo: Este trabalho trata da aplica¸c¿ao de funcionais de Lyapunov e Lyapunov-Krasovskii dependentes de parâmetro a alguns problemas selecionados da área de controle robusto, a saber: D-estabilidade robusta de polítipo de matrizes, D-estabilidade robusta de politopos de polinômios matriciais, estabilidade robusta de sistemas neutrais com atrasos variantes no tempo e controle robusto H8 de sistemas discretos no tempo com atraso nos estados. É utilizada a representação politópica para as incertezas dos sistemas estudados. São obtidas formulações convexas, na forma de desigualdades matriciais lineares, suficientes para a solução dos problemas selecionados. Essas condições podem ser resolvidas numericamente de maneira eficiente por meio de algoritmos especializados baseados em pontos interiores. Os resultados obtidos são menos conservadores que os encontrados na literatura, baseados em geral na estabilidade quadrática, isto é, as matrizes dos funcionais são fixas e independentes da incerteza<br>Abstract: This work deals with the application of parameter dependent Lyapunov and Lyapunov-Krasovskii functionals to some selected problems of robust control: robust D-stability of polytopes of matrices, robust D-stability of polytopes of polynomial matrices, robust stability of uncertain neutral systems with timevarying delays and robust H8 control of uncertain discrete time delay systems. The polytopic representation is used to describe the uncertainties. Convex formulations are obtained, in terms of inear matrix inequalities, that are sufficient for the solution of the selected problems. Those conditions can be solved in a efficient way through specialized interior point algorithms. The obtained results are less conservative than those from the literature, in general based on quadratic stability, i.e., the matrices in the functionals are fixed and do not depend on the uncertainty<br>Doutorado<br>Automação<br>Doutor em Engenharia Elétrica
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Borges, Renato Alves. "Controle e filtragem de sistemas lineares variantes no tempo por meio de funções de Lyapunov dependentes de parametros." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261054.
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Orientador: Pedro Luis Dias Peres<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-13T19:35:14Z (GMT). No. of bitstreams: 1
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Previous issue date: 2009<br>Resumo: A principal contribuição desta tese é a proposta de condições de sintese de filtros e controladores lineares, tanto robustos quanto dependentes de parametros, para sistemas discretos variantes no tempo.Os controladores, ou filtros, são obtidos solucionando problemas de otimização formulados em termos de desigualdades matriciais bililineares, por meio de um metodo que se baseia na alternancia de problemas convexos descritos por desigualdades matriciais lineares. Para obtenção das condiçoes de sintese foram utilizadas tanto funções de Lyapunov afins nos parâmetros quanto ametros, alem de variáveis multi-afins em diferentes instantes de tempo dos parâmetros, alem de variaveis extras introduzidas pelo lema de Finsler. Nesse contexto, sao tratados problemas de sintese com custo garantido H, assegurando robustez em relação a incertezas não estruturadas. Simulaçoes numéricas ilustram a eficiencia dos metodos propostos em termos de desempenho H quando comparados com outros metodos da literatura<br>Abstract: The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent)Lyapunov functions were usedto obtain the design conditions, as wellas extra variables introduced bythe Finsler's lemma.Design problems that take into account an H guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the effciency of the proposed methods in terms of H performance when compared with other strategies from the literature<br>Doutorado<br>Automação<br>Doutor em Engenharia Elétrica
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Zhebel, Elena. "A multigrid method with matrix-dependent transfer operators for 3D diffusion problems with jump coefficients." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:bsz:105-682918.
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Gegeben sei ein lineares Gleichungssystem $Au = f$ mit Koeffizientenmatrix $A$, welche eine spezielle block-tridiagonale Struktur besitzt. Solche lineare Gleichungssysteme entstehen bei der Diskretisierung dreidimensionaler elliptischer Randwertprobleme mit 7- oder 27-Punkte-Stern. In geophysikalischen Anwedungen, insbesondere bei Aufgaben aus der Geoelektrik, haben die Randwertprobleme unstetige Koeffizienten und sind meistens auf nicht-uniformen Gittern diskretisiert. Klassische geometrische Mehrgitterverfahren konvergieren um so langsamer, je stärker die Koeffizientensprünge ausfallen. Außerdem kann die Konvergenz durch die Variation der Gitterabstände beeinträchtigt werden. Zur Lösung wird ein matrix-abhängiges Mehrgitterverfahren vorgestellt. Als Glätter wird eine unvollständige Block LU-Zerlegung verwendet. Die Gittertransferoperationen werden anhand der Einträge der Matrix $A$ ermittelt. Das resultierende Verfahren erweist sich als sehr robust, insbesondere wenn es als Vorkonditionierung für das Verfahren der konjugierten Gradienten eingesetzt wird.
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Lichtner, Mark. "Exponential dichotomy and smooth invariant center manifolds for semilinear hyperbolic systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981306659.
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Howard, Leah. "Nets of order 4m+2: linear dependence and dimensions of codes." Thesis, 2009. http://hdl.handle.net/1828/1566.
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A k-net of order n is an incidence structure consisting of n2
points and nk lines. Two lines are said to be parallel if they do not intersect.
A k-net of order n satisfies the following four axioms: (i) every line contains n
points; (ii) parallelism is an equivalence relation on the set of lines; (iii) there
are k parallel classes, each consisting of n lines and (iv) any two non-parallel
lines meet exactly once.
A Latin square of order n is an n by n array of symbols in which each
row and column contains each symbol exactly once. Two Latin squares L
and M are said to be orthogonal if the n2 ordered pairs (Li,j , Mi,j ) are all
distinct. A set of t mutual ly orthogonal Latin squares is a collection of Latin
squares, necessarily of the same order, that are pairwise orthogonal. A k-net
of order n is combinatorially equivalent to k − 2 mutually orthogonal Latin
squares of order n. It is this equivalence that motivates much of the work in
this thesis.
One of the most important open questions in the study of Latin squares
is: given an order n what is the maximum number of mutually orthogonal
Latin squares of that order? This is a particularly interesting question when
n is congruent to two modulo four. A code is constructed from a net by
defining the characteristic vectors of lines to be generators of the code over
the finite field F2 . Codes allow the structure of nets to be profitably explored
using techniques from linear algebra.
In this dissertation a framework is developed to study linear dependence
in the code of the net N6 of order ten. A complete classification and combinatorial description of such dependencies is given. This classification could
facilitate a computer search for a net or could be used in conjunction with
more refined techniques to rule out the existence of these nets combinatorially. In more generality relations in 4-nets of order congruent to two modulo
four are also characterized.
One type of dependency determined algebraically is shown not to be combinatorially feasible in a net N6 of order ten. Some dependencies are shown
to be related geometrically, allowing for a concise classification.
Using a modification of the dimension argument first introduced by
Dougherty [19] new upper bounds are established on the dimension of codes
of nets of order congruent to two modulo four. New lower bounds on some
of these dimensions are found using a combinatorial argument. Certain constraints on the dimension of a code of a net are shown to imply the existence
of specific combinatorial structures in the net.
The problem of packing points into lines in a prescribed way is related
to packing problems in graphs and more general packing problems in combinatorics. This dissertation exploits the geometry of nets and symmetry
of complete multipartite graphs and combinatorial designs to further unify
these concepts in the context of the problems studied here.
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Roussel, Arnaud. "Tests pour la dépendance entre les sections dans un modèle de Poisson." Thèse, 2015. http://hdl.handle.net/1866/12487.
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Les simulations et figures ont été réalisées avec le logiciel R.<br>Pour des données de panel, les mesures répétées dans le temps peuvent remettre
en cause l’hypothèse d’indépendance entre les individus. Des tests ont été
développés pour pouvoir vérifier s’il reste de la dépendance entre les résidus d’un
modèle. Les trois tests que nous présentons dans ce mémoire sont ceux de Pesaran
(2004), Friedman (1937) et Frees (1995). Ces trois tests se basent sur les résidus
(et leurs corrélations) et ont été construits pour des modèles linéaires. Nous voulons
étudier dans ce mémoire les performances de ces trois tests dans le cadre d’un
modèle linéaire généralisé de Poisson. Dans ce but, on compare tout d’abord leurs
performances (niveaux et puissances) pour deux modèles linéaires, l’un ayant un
terme autorégressif et l’autre non. Par la suite, nous nous intéressons à leurs performances
pour un modèle linéaire généralisé de Poisson en s’inspirant de Hsiao,
Pesaran et Pick (2007) qui adaptent le test de Pesaran (2004) pour un modèle
linéaire généralisé. Toutes nos comparaisons de performances se feront à l’aide de
simulations dans lesquelles nous ferons varier un certain nombre de paramètres
(nombre d’observations, force de la dépendance, etc.). Nous verrons que lorsque
les corrélations sont toutes du même signe, le test de Pesaran donne en général
de meilleurs résultats, à la fois dans les cas linéaires et pour le modèle linéaire
généralisé. Le test de Frees présentera de bonnes propriétés dans le cas où le signe
des corrélations entre les résidus alterne.<br>For panel data, repeated measures over time can challenge the hypothesis of
dependence between subjects. Tests were developped in order to assess if some
dependence remains among residuals. The three tests we present in this master
thesis are from Pesaran (2004), Friedman (1937) and Frees (1995). These three
tests, constructed specifically for linear models, are based on the residuals generated
from models (and their correlations). We wish to study in this master thesis
the performances of these three tests in the case of generalized linear Poisson
models. For that goal, we compare them between each other (level, power, etc.)
using two linear models, one with an autoregressive term and the other without.
Next, inspired by Hsiao, Pesaran and Pick (2007) who adapt the test from Pesaran
(2004), we will study their performances in a generalized Poisson model.
All of our comparisons are done with simulations by modifying some variables
(number of observations, strength of the dependence). We will observe that when
the correlation is always of the same sign, Pesaran’s test is the best in most cases,
for the linear models and the generalized linear model. Frees’ test will show good
performances when the sign of the correlations alternates.
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Wannenwetsch, Jens [Verfasser]. "Lévy processes in finance : the change of measure and non-linear dependence / vorgelegt von Jens Wannenwetsch." 2005. http://d-nb.info/97602019X/34.
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"Magnetic Resonance Parameter Assessment from a Second Order Time-Dependent Linear Model." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.54899.
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abstract: This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method.<br>Dissertation/Thesis<br>Doctoral Dissertation Mathematics 2019
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"On safe tractable approximations of chance-constrained linear matrix inequalities with partly dependent perturbations." 2011. http://library.cuhk.edu.hk/record=b5894803.
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Cheung, Sin Shuen.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.<br>Includes bibliographical references (leaves 55-59).<br>Abstracts in English and Chinese.<br>Abstract --- p.i<br>Acknowledgement --- p.iii<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Preliminaries --- p.5<br>Chapter 2.1 --- Heuristics by Hoeffding and Janson --- p.5<br>Chapter 2.2 --- Facts in Matrix Theory --- p.10<br>Chapter 2.3 --- Facts in Probability --- p.11<br>Chapter 3 --- General Chance-Constrained LMIs --- p.18<br>Chapter 3.1 --- Probability Inequalities --- p.18<br>Chapter 3.2 --- Safe Tractable Approximations --- p.22<br>Chapter 4 --- Chance-Constrained Quadratically Perturbed LMIs --- p.27<br>Chapter 4.1 --- Exact Proper Fractional Covers --- p.27<br>Chapter 4.2 --- Bounding the Matrix Moment Generating Functions --- p.32<br>Chapter 5 --- Computational Study --- p.39<br>Chapter 5.1 --- Update Procedures for Safe Tractable Approximations --- p.39<br>Chapter 5.2 --- A Numerical Example and Comparisons --- p.44<br>Chapter 6 --- Conclusion --- p.54<br>Bibliography --- p.55
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Nassaj, Feras [Verfasser]. "Modeling linearly and non-linearly dependent simulation input data / vorgelegt von Feras Nassaj." 2010. http://d-nb.info/1008247561/34.
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Chaimoon, Krit Civil & Environmental Engineering Faculty of Engineering UNSW. "Numerical simulation of fracture in unreinforced masonry." 2007. http://handle.unsw.edu.au/1959.4/40757.
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The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.
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Scoleri, Tony. "Fundamental numerical schemes for parameter estimation in computer vision." 2008. http://hdl.handle.net/2440/50726.
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An important research area in computer vision is parameter estimation. Given a mathematical model and a sample of image measurement data, key parameters are sought to encapsulate geometric properties of a relevant entity. An optimisation problem is often formulated in order to find these parameters. This thesis presents an elaboration of fundamental numerical algorithms for estimating parameters of multi-objective models of importance in computer vision applications. The work examines ways to solve unconstrained and constrained minimisation problems from the view points of theory, computational methods, and numerical performance. The research starts by considering a particular form of multi-equation constraint function that characterises a wide class of unconstrained optimisation tasks. Increasingly sophisticated cost functions are developed within a consistent framework, ultimately resulting in the creation of a new iterative estimation method. The scheme operates in a maximum likelihood setting and yields near-optimal estimate of the parameters. Salient features of themethod are that it has simple update rules and exhibits fast convergence. Then, to accommodate models with functional dependencies, two variant of this initial algorithm are proposed. These methods are improved again by reshaping the objective function in a way that presents the original estimation problem in a reduced form. This procedure leads to a novel algorithm with enhanced stability and convergence properties. To extend the capacity of these schemes to deal with constrained optimisation problems, several a posteriori correction techniques are proposed to impose the so-called ancillary constraints. This work culminates by giving two methods which can tackle ill-conditioned constrained functions. The combination of the previous unconstrained methods with these post-hoc correction schemes provides an array of powerful constrained algorithms. The practicality and performance of themethods are evaluated on two specific applications. One is planar homography matrix computation and the other trifocal tensor estimation. In the case of fitting a homography to image data, only the unconstrained algorithms are necessary. For the problem of estimating a trifocal tensor, significant work is done first on expressing sets of usable constraints, especially the ancillary constraints which are critical to ensure that the computed object conforms to the underlying geometry. Evidently here, the post-correction schemes must be incorporated in the computational mechanism. For both of these example problems, the performance of the unconstrained and constrained algorithms is compared to existing methods. Experiments reveal that the new methods perform with high accuracy to match a state-of-the-art technique but surpass it in execution speed.<br>Thesis (Ph.D.) - University of Adelaide, School of Mathemtical Sciences, Discipline of Pure Mathematics, 2008
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Zhebel, Elena. "A multigrid method with matrix-dependent transfer operators for 3D diffusion problems with jump coefficients." Doctoral thesis, 2001. https://tubaf.qucosa.de/id/qucosa%3A22680.
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Gegeben sei ein lineares Gleichungssystem $Au = f$ mit Koeffizientenmatrix $A$, welche eine spezielle block-tridiagonale Struktur besitzt. Solche lineare Gleichungssysteme entstehen bei der Diskretisierung dreidimensionaler elliptischer Randwertprobleme mit 7- oder 27-Punkte-Stern. In geophysikalischen Anwedungen, insbesondere bei Aufgaben aus der Geoelektrik, haben die Randwertprobleme unstetige Koeffizienten und sind meistens auf nicht-uniformen Gittern diskretisiert. Klassische geometrische Mehrgitterverfahren konvergieren um so langsamer, je stärker die Koeffizientensprünge ausfallen. Außerdem kann die Konvergenz durch die Variation der Gitterabstände beeinträchtigt werden. Zur Lösung wird ein matrix-abhängiges Mehrgitterverfahren vorgestellt. Als Glätter wird eine unvollständige Block LU-Zerlegung verwendet. Die Gittertransferoperationen werden anhand der Einträge der Matrix $A$ ermittelt. Das resultierende Verfahren erweist sich als sehr robust, insbesondere wenn es als Vorkonditionierung für das Verfahren der konjugierten Gradienten eingesetzt wird.
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Klimanis, Nils. "Generic Programming and Algebraic Multigrid for Stabilized Finite Element Methods." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B38C-5.
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