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Tesi sul tema "Nonlinear eigenvalue problems"

Autore: Grafiati
Pubblicato: 4 giugno 2021
Ultima modifica: 26 aprile 2022

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1

Lippert, Ross Adams. "Nonlinear eigenvalue problems." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50013.

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2

Tretter, Christiane. "On l-nonlinear [lambda-nonlinear] boundary eigenvalue problems /." Berlin : Akad.-Verl, 1993. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=004392929&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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3

Elssel, Kolja. "Automated multilevel substructuring for nonlinear eigenvalue problems." Berlin dissertation.de, 2006. http://deposit.d-nb.de/cgi-bin/dokserv?id=2887072&prov=M&dok_var=1&dok_ext=htm.

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4

Brennan, Michael C. "Rational Interpolation Methods for Nonlinear Eigenvalue Problems." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/84924.

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This thesis investigates the numerical treatment of nonlinear eigenvalue problems. These problems are defined by the condition $T(lambda) v = boldsymbol{0}$, with $T: C to C^{n times n}$, where we seek to compute the scalar-vector pairs, $lambda in C$ and nonzero $ v in C^{n}$. The first contribution of this work connects recent contour integration methods to the theory and practice of system identification. This observation leads us to explore rational interpolation for system realization, producing a Loewner matrix contour integration technique. The second development of this work studies th
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5

Akinola, Richard O. "Numerical solution of linear and nonlinear eigenvalue problems." Thesis, University of Bath, 2010. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.520903.

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Given a real parameter-dependent matrix, we obtain an algorithm for computing the value of the parameter and corresponding eigenvalue for which two eigenvalues of the matrix coalesce to form a 2-dimensional Jordan block. Our algorithms are based on extended versions of the implicit determinant method of Spence and Poulton [55]. We consider when the eigenvalue is both real and complex, which results in solving systems of nonlinear equations by Newton’s or the Gauss-Newton method. Our algorithms rely on good initial guesses, but if these are available, we obtain quadratic convergence. Next, we d
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6

Solov'ëv, Sergey I. "Preconditioned iterative methods for monotone nonlinear eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600657.

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This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue probl
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7

Solov'ëv, Sergey I. "Preconditioned iterative methods for a class of nonlinear eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601389.

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In this paper we develop new preconditioned iterative methods for solving monotone nonlinear eigenvalue problems. We investigate the convergence and derive grid-independent error estimates for these methods. Numerical experiments demonstrate the practical effectiveness of the proposed methods for a model problem.
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8

Betcke, Marta. "Iterative projection methods for symmetric nonlinear eigenvalue problems with applications." Berlin dissertation.de, 2007. http://www.dissertation.de/buch.php3?buch=5233.

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9

Bari, Rehana. "Local and global bifurcation theory for multiparameter nonlinear eigenvalue problems." Thesis, Heriot-Watt University, 1995. http://hdl.handle.net/10399/755.

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10

Lindsay, Alan Euan. "Topics in the asymptotic analysis of linear and nonlinear eigenvalue problems." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/26271.

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In Applied Mathematics, linear and nonlinear eigenvalue problems arise frequently when characterizing the equilibria of various physical systems. In this thesis, two specific problems are studied, the first of which has its roots in micro engineering and concerns Micro-Electro Mechanical Systems (MEMS). A MEMS device consists of an elastic beam deflecting in the presence of an electric field. Modelling such devices leads to nonlinear eigenvalue problems of second and fourth order whose solution properties are investigated by a variety of asymptotic and numerical techniques. The second probl
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11

Rehbein, Nicolai [Verfasser]. "Inexact Iterative Projection Methods for Linear and Nonlinear Eigenvalue Problems / Nicolai Rehbein." München : Verlag Dr. Hut, 2020. http://d-nb.info/1219476250/34.

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12

Moradifam, Amir. "Hardy-Rellich inequalities and the critical dimension of fourth order nonlinear elliptic eigenvalue problems." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/27775.

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This thesis consists of three parts and manuscripts of seven research papers studying improved Hardy and Hardy-Rellich inequalities, nonlinear eigenvalue problems, and simultaneous preconditioning and symmetrization of linear systems. In the first part that consists of three research papers we study improved Hardy and Hardy-Rellich inequalities. In sections 2 and 3, we give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in Rn, n ≥ 1, so that the following inequalities hold for all u \in C_{0}^{\infty}(B): \begin{equation*} \label{o
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13

Ali, Ali Hasan. "Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.

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14

Rehbein, Nicolai [Verfasser], and Heinrich [Akademischer Betreuer] Voß. "Inexact iterative projection methods for linear and nonlinear eigenvalue problems / Nicolai Rehbein ; Betreuer: Heinrich Voß." Hamburg : Universitätsbibliothek der Technischen Universität Hamburg-Harburg, 2020. http://d-nb.info/1206999136/34.

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15

Maad, Sara. "Critical point theory with applications to semilinear problems without compactness." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1557-2/.

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16

Grimm, Alexander Rudolf. "Parametric Dynamical Systems: Transient Analysis and Data Driven Modeling." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/83840.

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Abstract (sommario):
Dynamical systems are a commonly used and studied tool for simulation, optimization and design. In many applications such as inverse problem, optimal control, shape optimization and uncertainty quantification, those systems typically depend on a parameter. The need for high fidelity in the modeling stage leads to large-scale parametric dynamical systems. Since these models need to be simulated for a variety of parameter values, the computational burden they incur becomes increasingly difficult. To address these issues, parametric reduced models have encountered increased popularity in recent y
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17

Dragana, Gardašević. "Lokalizacije Geršgorinovog tipa za nelinearne probleme karakterističnih korena." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2019. https://www.cris.uns.ac.rs/record.jsf?recordId=108416&source=NDLTD&language=en.

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Predmet istraživanja u doktorskoj disertaciji je metoda za konstrukcijulokalizacionih skupova za spektar i pseudospektar nelinearnih problemakarakterističnih korena bazirana na Geršgorinovoj teoremi i njenimgeneralizacijama koja koristi osobine poznatih podklasa H-matrica.Navedena tvrđenja i primeri rasvetljavaju odnose između navedenihlokalizacionih skupova, što je posebno značajno za primenu u praksi.Sadržaj ovog rada time predstavlja polaznu tačku za dublja istraživanja natemu konstrukcije lokalizacionih skupova za spektar i pseudospektarnelinearnih problema karakterističnih korena Geršgori
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18

Lázaro, Navarro Mario. "The Eigenvalue Problem in Linear Viscoelastic Structures: New Numerical Approaches and the Equivalent Viscous Model." Doctoral thesis, Universitat Politècnica de València, 2013. http://hdl.handle.net/10251/30062.

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El análisis y el control de las vibraciones cobra especial importancia en muchas ramas de la ingeniería, en especial la ingeniería mecánica, civil, aeronáutica y automovilística. Tal es así que prácticamente se identi¿ca como un área independiente dentro del análisis dinámico de estructuras. Desde los comienzos de esta teoría, las fuerzas disipativas o de amortiguamiento han sido uno de los fenómenos más difíciles de modelizar. El modelo viscoso, por su sencillez y versatilidad ha sido y sigue siendo el gran paradigma de los modelos de amortiguamiento. Sin embargo, como consecuencia de la
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19

Sharify, Meisam. "Algorithmes de mise à l'échelle et méthodes tropicales en analyse numérique matricielle." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00643836.

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L'Algèbre tropicale peut être considérée comme un domaine relativement nouveau en mathématiques. Elle apparait dans plusieurs domaines telles que l'optimisation, la synchronisation de la production et du transport, les systèmes à événements discrets, le contrôle optimal, la recherche opérationnelle, etc. La première partie de ce manuscrit est consacrée a l'étude des applications de l'algèbre tropicale à l'analyse numérique matricielle. Nous considérons tout d'abord le problème classique de l'estimation des racines d'un polynôme univarié. Nous prouvons plusieurs nouvelles bornes pour la valeur
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20

Potts, Daniel, and Manfred Tasche. "Parameter estimation for nonincreasing exponential sums by Prony-like methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-86476.

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For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.
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21

Akoussan, Komlan. "Modélisation et conception de structures composites viscoélastiques à haut pouvoir amortissant." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0188/document.

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L’objectif de ce travail est de développer des outils numériques utilisables dans la détermination de manière exacte des propriétés modales des structures sandwichs viscoélastiques composites au vue de la conception des structures sandwichs viscoélastiques légères mais à haut pouvoir amortissant. Pour cela nous avons tout d’abord développé un outil générique implémenté en Matlab pour la détermination des propriétés modales en vibration libre des plaques sandwichs viscoélastiques dont les faces sont en stratifié de plusieurs couches orientées dans diverses directions. L’intérêt de cet outil, ba
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22

POMERANZ, SHIRLEY BARBARA. "COMPUTATIONAL METHODS FOR NONLINEAR ELLIPTIC EIGENVALUE PROBLEMS." 1987. https://scholarworks.umass.edu/dissertations/AAI8727097.

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A basic problem is that of finding nontrivial solutions of the following nonlinear eigenvalue problem: $-\Delta$u = $\lambda$F$\prime$ (u) in D, u = 0 on $\partial$D, where D is a domain in R$\sp{\rm N}$, N = 1,2,3, and F$\prime$(u) is non-monotone. Problems of this kind arise, for example, in plasma physics, fluid dynamics, and astrophysics. In the first part of this thesis, an equivalent variational formulation is used to obtain an iterative procedure for solving the problem with a general function F(u). The global convergence of this procedure is established, i.e., convergence from any init
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23

Skrzypczak, Iwona. "Hardy–type inequalities and nonlinear eigenvalue problems." Doctoral thesis, 2013.

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Abstract (sommario):
Naszym celem jest wprowadzenie nowej metody konstruowania nier´owno´sci typu Hardy’ego. Konstruujemy je znaj¸ac rozwi¸azania u zagadnie´n p oraz A– harmonicznych. Wyprowadzamy nier´owno´sci typu Caccioppoli dla u. Jako wniosek z nich otrzymujemy wa˙zone nier´owno´sci typu Hardy’ego dla funkcji Lipschitzowskich o zwartym no´sniku.
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24

Tu, Hui-Juan, and 杜慧絹. "Multigrid-Finite Element Methods for Nonlinear Eigenvalue Problems." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/18663085309822531813.

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碩士<br>國立中興大學<br>應用數學系<br>91<br>We study multigrid methods in the context of continuation methods for nonlinear elliptic eigenvalue problems. Here we use the finite element method to discretize the problems. The Lanczos method is used as the relaxation scheme for the V-cycle, W-cycle and full multigrid V-cycle schemes, respectively. Some multigrid-continuation algorithms are proposed for tracing the solution curves in the nonlinear elliptic eigenvalue problems. Our numerical results show the algorithms we propose are efficient. Finally, some concluding remarks are given.
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25

Chen, M. J., and 陳明哲. "A Parallel Continuation Algorithm for Nonlinear Eigenvalue Problems." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/24272844833796626703.

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碩士<br>國立中興大學<br>應用數學研究所<br>81<br>We describe a parallel continuation algorithm for the numeri- cal treatment of certain semilinear eigenvalue problems with Dirichlet boundary conditions. The computations were executed on a TRANSPUTER, a distributed memory multiprocessor. The nu- merical results show that our algorithm is quite competitive, and may be applied to various nonlinear eigenvalue problems.
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26

Chang, Shing-Lin, and 張勝麟. "Multigrid and Domain Decomposition for Nonlinear Elliptic Eigenvalue Problems." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/64948007317732813486.

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博士<br>國立中興大學<br>應用數學系<br>90<br>We study some iterative methods (such as the Lanczos method, GMRES and their other variants) and domain decomposition methods for solving nonlinear elliptic eigenvalue problems. First, we apply the Lanczos method to solve linear systems with multiple right hand side. We give an error bound for the approximate solution of the second linear system, where the Lanczos-Galerkin process is used to solve the first linear system. We also seek the possible application of the proposed numerical method to continuation problems. Next, we show some convergence theory for the
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27

Liao, Shih-Pei, and 廖詩佩. "Multigrid-type Inverse Iteration Algorithms for Nonlinear Eigenvalue Problems." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/01905478258647078308.

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碩士<br>國立交通大學<br>應用數學系<br>88<br>The article is concerned with aspects of the nonlinear eigenvalue problems which arise from partial differential equation by finite difference discretization: T(λ)x=0, where T(λ) is a n ×n matrix whose elements are analytical functions in parameter λ. We shall propose the multigrid type inverse iteration algorithms which use the multigrid linear solver for finding the smallest eigenvalue in magnitude of the nonlinear eigenvalue problem and grid transform strategy for finding the initial vector. The methods fi
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28

Lin, Ya Jing, and 林雅菁. "Multigrid and two-grid discretization schemes for nonlinear eigenvalue problems." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/56669185651563914324.

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碩士<br>國立中興大學<br>應用數學系<br>92<br>We study multigrid methods in the context of continuation methods for semilinear elliptic eigenvalue problems, where the Lanczos method, the MINRES and the SYMMLQ are used as linear solvers. The semilinear elliptic eigenvalue problems are discretized by six-node triangular elements. We compare the efficiency of these linear solvers in the context of multigrid V-cycle, W-cycle and the full multigrid V-cycle (FMG) schemes. Next, we study the two-grid centered difference discretization scheme for the eigenvalue problem defined on an
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29

Schreiber, Kathrin [Verfasser]. "Nonlinear eigenvalue problems: Newton-type methods and nonlinear Rayleigh functionals / vorgelegt von Kathrin Schreiber." 2008. http://d-nb.info/989504999/34.

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30

Shou, Jon-Ping, and 邵仲平. "The Bifurcation and Continuation of Solution Path of Nonlinear Eigenvalue Problems." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/41830895705997268646.

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碩士<br>輔仁大學<br>數學系研究所<br>84<br>In this thesis,we use numerical methods which including central difference met hod,Newton''s iteration method,pesudo-arclength method and finite dimensional L iapunov-Schmidt deflation method,and discuss both continuation and bifurcation of solution path in the nonlinear eigenvalue problems of nonlinear bifurcatio n problems compound with the basis of bifurcation theory-implicit function the orem. At the same time,we research several mathematics models such as Rod bucl ing p
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31

江俊瑩. "How close can we approach singular points in nonlinear eigenvalue problems." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/03349048785939168936.

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碩士<br>國立中興大學<br>應用數學系<br>90<br>We study multigrid methods in the context of continuation methods for semilinear elliptic eigenvalue problems, where the Lanczos method and its variant MINRES are used as the relaxation scheme for the V-cycle, W-cycle and full multigrid V-cycle schemes, respectively. Since the GMRES method is a generalization of the MINRES algorithm, the results of Brown and Walker \cite{BW} can be exploited to solve nearly singular symmetric linear systems that occur in continuation problems. We give some error bounds for the MINRES algorithm which are more accurate than those
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32

Moletsane, Boitumelo. "Spectral properties of a fourth order differential equation with eigenvalue dependent boundary conditions." Thesis, 2012. http://hdl.handle.net/10539/11340.

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33

Chen, Chao-Nien. "Multiple solutions and bifurcation for a class of nonlinear Sturm-Liouville eigenvalue problems on an unbounded domain." 1988. http://catalog.hathitrust.org/api/volumes/oclc/18661411.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1988.<br>Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 122-126).
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34

Abdel-Aziz, Mohammedi Radwan Hassan. "Numerical safeguarded use of the implicit restarted Lanczos algorithm for solving nonlinear eigenvalue problems and its monotonicity analysis." Thesis, 1993. http://hdl.handle.net/1911/16596.

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In this thesis, we develop an efficient accurate numerical algorithm for evaluating a few of the smallest eigenvalues and their corresponding eigenvectors for large scale nonlinear eigenproblems. The entries of the matrices in these problems are transcendental functions approximated well by rational functions. This algorithm is based upon the Implicit Restarted Lanczos method for solving the linear eigenvalue sub-problems that arise in conjunction with a new zero-finding technique that uses rational function interpolation to approximate the generalized eigenvalues. We have tested this techniqu
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35

Wei, Bo-Cheng, and 魏柏丞. "Tailored Finite Point Method and Continuation Method for Solving a Nonlinear Schrodinger Eigenvalue Problem." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/77831501474497560667.

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碩士<br>國立中興大學<br>應用數學系所<br>100<br>We study a Tailored Finite Point Method (TFPM) and predictor-corrector continuation method for solving eigenvalue problems include simple linear eigenvalue problem, nonlinear eigenvalue problem, linear Schrodinger eigenvalue problem, nonlinear Schrodinger eigenvalue problem, and coupled nonlinear Schrodinger eigenvalue problem. First, we present a tailored finite point method to discretize above equa- tions, and trace the solution curve by predictor-corrector continuation method. The numerical results of the problem with exact solution show that error for TFPM
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36

Wang, Changchun. "On Computing Multiple Solutions of Nonlinear PDEs Without Variational Structure." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11171.

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Variational structure plays an important role in critical point theory and methods. However many differential problems are non-variational i.e. they are not the Euler- Lagrange equations of any variational functionals, which makes traditional critical point approach not applicable. In this thesis, two types of non-variational problems, a nonlinear eigen solution problem and a non-variational semi-linear elliptic system, are studied. By considering nonlinear eigen problems on their variational energy profiles and using the implicit function theorem, an implicit minimax method is developed for
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