@phdthesis{Baumann2008,
  author    = {Baumann, Markus},
  title     = {Newton's Method for Path-Following Problems on Manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28099},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {Many optimization problems for a smooth cost function f on a manifold M can be solved by determining the zeros of a vector field F; such as e.g. the gradient F of the cost function f. If F does not depend on additional parameters, numerous zero-finding techniques are available for this purpose. It is a natural generalization however, to consider time-dependent optimization problems that require the computation of time-varying zeros of time-dependent vector fields F(x,t). Such parametric optimization problems arise in many fields of applied mathematics, in particular path-following problems in robotics, recursive eigenvalue and singular value estimation in signal processing, as well as numerical linear algebra and inverse eigenvalue problems in control theory. In the literature, there are already some tracking algorithms for these tasks, but these do not always adequately respect the manifold structure. Hence, available tracking results can often be improved by implementing methods working directly on the manifold. Thus, intrinsic methods are of interests that evolve during the entire computation on the manifold. It is the task of this thesis, to develop such intrinsic zero finding methods. The main results of this thesis are as follows: - A new class of continuous and discrete tracking algorithms is proposed for computing zeros of time-varying vector fields on Riemannian manifolds. This was achieved by studying the newly introduced time-varying Newton Flow and the time-varying Newton Algorithm on Riemannian manifolds. - Convergence analysis is performed on arbitrary Riemannian manifolds. - Concretization of these results on submanifolds, including for a new class of algorithms via local parameterizations. - More specific results in Euclidean space are obtained by considering inexact and underdetermined time-varying Newton Flows. - Illustration of these newly introduced algorithms by examining time-varying tracking tasks in three application areas: Subspace analysis, matrix decompositions (in particular EVD and SVD) and computer vision.},
  subject      = {Dynamische Optimierung},
  language  = {en}
}
@phdthesis{Pechmann2008,
  author    = {Pechmann, Patrick R.},
  title     = {Penalized Least Squares Methoden mit st{\"u}ckweise polynomialen Funktionen zur L{\"o}sung von partiellen Differentialgleichungen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28136},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {Das Hauptgebiet der Arbeit stellt die Approximation der L{\"o}sungen partieller Differentialgleichungen mit Dirichlet-Randbedingungen durch Splinefunktionen dar. Partielle Differentialgleichungen finden ihre Anwendung beispielsweise in Bereichen der Elektrostatik, der Elastizit{\"a}tstheorie, der Str{\"o}mungslehre sowie bei der Untersuchung der Ausbreitung von W{\"a}rme und Schall. Manche Approximationsaufgaben besitzen keine eindeutige L{\"o}sung. Durch Anwendung der Penalized Least Squares Methode wurde gezeigt, dass die Eindeutigkeit der gesuchten L{\"o}sung von gewissen Minimierungsaufgaben sichergestellt werden kann. Unter Umst{\"a}nden l{\"a}sst sich sogar eine h{\"o}here Stabilit{\"a}t des numerischen Verfahrens gewinnen. F{\"u}r die numerischen Betrachtungen wurde ein umfangreiches, effizientes C-Programm erstellt, welches die Grundlage zur Best{\"a}tigung der theoretischen Voraussagen mit den praktischen Anwendungen bildete.},
  subject      = {Approximationstheorie},
  language  = {de}
}
@phdthesis{Solak2007,
  author    = {Solak, Ebru},
  title     = {Almost Completely Decomposable Groups of Type (1,2)},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-24794},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {A torsion free abelian group of finite rank is called almost completely decomposable if it has a completely decomposable subgroup of finite index. A p-local, p-reduced almost completely decomposable group of type (1,2) is briefly called a (1,2)-group. Almost completely decomposable groups can be represented by matrices over the ring Z/hZ, where h is the exponent of the regulator quotient. This particular choice of representation allows for a better investigation of the decomposability of the group. Arnold and Dugas showed in several of their works that (1,2)-groups with regulator quotient of exponent at least p^7 allow infinitely many isomorphism types of indecomposable groups. It is not known if the exponent 7 is minimal. In this dissertation, this problem is addressed.},
  language  = {en}
}
@phdthesis{Lageman2007,
  author    = {Lageman, Christian},
  title     = {Convergence of gradient-like dynamical systems and optimization algorithms},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-23948},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {This work studies the convergence of trajectories of gradient-like systems. In the first part of this work continuous-time gradient-like systems are examined. Results on the convergence of integral curves of gradient systems to single points of Lojasiewicz and Kurdyka are extended to a class of gradient-like vector fields and gradient-like differential inclusions. In the second part of this work discrete-time gradient-like optimization methods on manifolds are studied. Methods for smooth and for nonsmooth optimization problems are considered. For these methods some convergence results are proven. Additionally the optimization methods for nonsmooth cost functions are applied to sphere packing problems on adjoint orbits.},
  subject      = {Dynamisches System},
  language  = {en}
}
@phdthesis{Klug2006,
  author    = {Klug, Andreas},
  title     = {Affine-Scaling Methods for Nonlinear Minimization Problems and Nonlinear Systems of Equations with Bound Constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18851},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {In this thesis affine-scaling-methods for two different types of mathematical problems are considered. The first type of problems are nonlinear optimization problems subject to bound constraints. A class of new affine-scaling Newton-type methods is introduced. The methods are shown to be locally quadratically convergent without assuming strict complementarity of the solution. The new methods differ from previous ones mainly in the choice of the scaling matrix. The second type of problems are semismooth system of equations with bound constraints. A new affine-scaling trust-region method for these problems is developed. The method is shown to have strong global and local convergence properties under suitable assumptions. Numerical results are presented for a number of problems arising from different areas.},
  subject      = {Skalierungsfunktion},
  language  = {en}
}
@phdthesis{Petra2006,
  author    = {Petra, Stefania},
  title     = {Semismooth least squares methods for complementarity problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18660},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {This thesis is concerned with numerical methods for solving nonlinear and mixed complementarity problems. Such problems arise from a variety of applications such as equilibria models of economics, contact and structural mechanics problems, obstacle problems, discrete-time optimal control problems etc. In this thesis we present a new formulation of nonlinear and mixed complementarity problems based on the Fischer-Burmeister function approach. Unlike traditional reformulations, our approach leads to an over-determined system of nonlinear equations. This has the advantage that certain drawbacks of the Fischer-Burmeister approach are avoided. Among other favorable properties of the new formulation, the natural merit function turns out to be differentiable. To solve the arising over-determined system we use a nonsmooth damped Levenberg-Marquardt-type method and investigate its convergence properties. Under mild assumptions, it can be shown that the global and local fast convergence results are similar to some of the better equation-based method. Moreover, the new method turns out to be significantly more robust than the corresponding equation-based method. For the case of large complementarity problems, however, the performance of this method suffers from the need for solving the arising linear least squares problem exactly at each iteration. Therefore, we suggest a modified version which allows inexact solutions of the least squares problems by using an appropriate iterative solver. Under certain assumptions, the favorable convergence properties of the original method are preserved. As an alternative method for mixed complementarity problems, we consider a box constrained least squares formulation along with a projected Levenberg-Marquardt-type method. To globalize this method, trust region strategies are proposed. Several ingredients are used to improve this approach: affine scaling matrices and multi-dimensional filter techniques. Global convergence results as well as local superlinear/quadratic convergence are shown under appropriate assumptions. Combining the advantages of the new methods, a new software for solving mixed complementarity problems is presented.},
  subject      = {Komplementarit{\"a}tsproblem},
  language  = {en}
}
@phdthesis{Michel2006,
  author    = {Michel, Ren{\´e}},
  title     = {Simulation and Estimation in Multivariate Generalized Pareto Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18489},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {The investigation of multivariate generalized Pareto distributions (GPDs) in the framework of extreme value theory has begun only lately. Recent results show that they can, as in the univariate case, be used in Peaks over Threshold approaches. In this manuscript we investigate the definition of GPDs from Section 5.1 of Falk et al. (2004), which does not differ in the area of interest from those of other authors. We first show some theoretical properties and introduce important examples of GPDs. For the further investigation of these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. This algorithm is based on the Shi transformation, which was introduced by Shi (1995) and was used in Stephenson (2003) for the simulation of multivariate extreme value distributions of logistic type. We also present nonparametric and parametric estimation methods in GPD models. We estimate the angular density nonparametrically in arbitrary dimension, where the bivariate case turns out to be a special case. The asymptotic normality of the corresponding estimators is shown. Also in the parametric estimations, which are mainly based on maximum likelihood methods, the asymptotic normality of the estimators is shown under certain regularity conditions. Finally the methods are applied to a real hydrological data set containing water discharges of the rivers Altm{\"u}hl and Danube in southern Bavaria.},
  subject      = {Pareto-Verteilung},
  language  = {en}
}
@book{FalkMarohnMicheletal.2006,
  author    = {Falk, Michael and Marohn, Frank and Michel, Ren{\´e} and Hofmann, Daniel and Macke, Maria and Tewes, Bernward and Dinges, Peter},
  title     = {A First Course on Time Series Analysis : Examples with SAS},
  organization    = {Universit{\"a}t W{\"u}rzburg / Lehrstuhl f{\"u}r Statistik},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-16919},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License.},
  subject      = {Zeitreihenanalyse},
  language  = {en}
}
@phdthesis{Kleinsteuber2005,
  author    = {Kleinsteuber, Martin},
  title     = {Jacobi-type methods on semisimple Lie algebras : a Lie algebraic approach to numerical linear algebra},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-16454},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {Es wird eine Lie-algebraische Verallgemeinerung sowohl des klassischen als auch des Sortier-Jacobi-Verfahrens f{\"u}r das symmetrische Eigenwertproblem behandelt. Der koordinatenfreie Zugang erm{\"o}glicht durch eine neue Betrachtungsweise die Vereinheitlichung strukturierter Eigen- und Singul{\"a}rwertprobleme, darunter bis dato noch nicht betrachtete F{\"a}lle. F{\"u}r beide Verfahren wird lokal quadratische Konvergenz, sowohl f{\"u}r den regul{\"a}ren als auch f{\"u}r den irregul{\"a}ren Fall, gezeigt. Die Analyse und Verallgemeinerung der sog. speziellen Sweeps f{\"u}r das symmetrische Eigenwertproblem f{\"u}hrt zu neuen Sweep-Methoden f{\"u}r strukturierte Eigen- und Singul{\"a}rwertprobleme, die ein besseres Konvergenzverhalten als die bisher bekannten aufweisen.},
  subject      = {Eigenwert},
  language  = {en}
}
@phdthesis{Vodopivec2005,
  author    = {Vodopivec, Andrija},
  title     = {Quasibasen abelscher, nichtseparabler p-Gruppen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-15359},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {In dieser Arbeit wird der Bau der (abz{\"a}hlbaren) abelschen p-Gruppen untersucht, durch die Betrachtung der dazugeh{\"o}rigen Quasibasen, die als bestimmte erzeugende Systeme der gegebenen p-Gruppe definiert sind. Die Untersuchung wird insbesondere auf die nichtseparablen p-Gruppen und ihre induktiven Quasibasen bezogen.},
  subject      = {Abelsche p-Gruppe},
  language  = {de}
}