@phdthesis{Ramsauer2005, author = {Ramsauer, Markus}, title = {Energie- und qualit{\"a}tsbewußte Einplanung von periodischen Prozessen in eingebetteten Echtzeitsystemen}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-628}, school = {Universit{\"a}t Passau}, year = {2005}, abstract = {Mobile Ger{\"a}te dienen immer h{\"a}ufiger zur Ausf{\"u}hrung von Echtzeitanwendungen, sie bieten immer mehr Rechenleistung und sie werden kleiner und leichter. Hohe Rechenleistung erfordert jedoch sehr viel Energie, was im Gegensatz zu den geringen Akkukapazit{\"a}ten, die aus der Forderung nach kleinen und leichten Ger{\"a}ten resultieren, steht. Bei der Echtzeiteinplanung von Rechenprozessen gewinnt daher der Energieverbrauch der Ger{\"a}te neben der rechtzeitigen Beendigung von Anwendungen zunehmend an Bedeutung, weil sie m{\"o}glichst lange unabh{\"a}ngig vom Stromnetz betrieben werden sollen. Andererseits werden auf diesen Ger{\"a}ten rechenintensive Anwendungen ausgef{\"u}hrt, bei denen es w{\"u}nschenswert ist, die maximale mit der verf{\"u}gbaren Rechenleistung erzielbare Qualit{\"a}t zu erhalten. In dieser Arbeit wird ein Systemmodell vorgestellt, das den Design-to-time-Ansatz mit den M{\"o}glichkeiten der dynamischen Leistungsanpassung (Rechenleistung und verbrauchte elektrische Leistung) moderner Prozessoren vereinigt. Der Design-to-time-Ansatz erm{\"o}glicht Energieeinsparungen oder Qualit{\"a}tssteigerungen durch die dynamische Auswahl alternativer Implementierungen, welche dieselbe Aufgabe mit unterschiedlicher Ausf{\"u}hrungsdauer und Qualit{\"a}t bzw. Energieverbrauch erf{\"u}llen. Das Systemmodell umfaßt unter anderem periodische Prozesse mit harten Echtzeitbedingungen, Datenabh{\"a}ngigkeiten und alternativen Implementierungen, sowie Prozessoren mit diskreten Leistungsstufen. Die Einplanung der Prozesse erfolgt in zwei Phasen. In der Offline-Phase wird ein flexibler Schedule berechnet, der f{\"u}r die zur Laufzeit m{\"o}glichen Kombinationen von verstrichener Zeit und noch einzuplanender Prozeßmenge den jeweils einzuplanenden Prozeß, sowie die zu verwendende Implementierung und gegebenenfalls die einzustellende Leistungsstufe beinhaltet. Dieser flexible Schedule wird w{\"a}hrend der Online-Phase mit vernachl{\"a}ssigbarem Zeit- und Energieaufwand von einem Scheduler interpretiert. F{\"u}r die Berechnung der optimalen flexiblen Schedules wurde ein Optimierer entwickelt, der eine Folge von flexiblen Schedules mit monoton steigender G{\"u}te (niedriger Energieverbrauch bzw. hohe Qualit{\"a}t) generiert, und damit der Klasse der Anytime-Algorithmen zuzuordnen ist. Eine Variante der Dynamischen Programmierung dient zur Bestimmung global optimaler, flexibler Schedules, die beispielsweise als Basis f{\"u}r Benchmarks dienen. Eine auf Simulated Annealing basierende Variante des Optimierers erm{\"o}glicht ein schnelleres Auffinden guter, flexibler Schedules f{\"u}r umfangreichere Anwendungen.}, subject = {Echtzeitsystem}, language = {de} } @phdthesis{Limbeck2013, author = {Limbeck, Jan}, title = {Computation of Approximate Border Bases and Applications}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-27197}, school = {Universit{\"a}t Passau}, year = {2013}, abstract = {This thesis addresses some of the algorithmic and numerical challenges associated with the computation of approximate border bases, a generalisation of border bases, in the context of the oil and gas industry. The concept of approximate border bases was introduced by D. Heldt, M. Kreuzer, S. Pokutta and H. Poulisse in "Approximate computation of zero-dimensional polynomial ideals" as an effective mean to derive physically relevant polynomial models from measured data. The main advantages of this approach compared to alternative techniques currently in use in the (hydrocarbon) industry are its power to derive polynomial models without additional a priori knowledge about the underlying physical system and its robustness with respect to noise in the measured input data. The so-called Approximate Vanishing Ideal (AVI) algorithm which can be used to compute approximate border bases and which was also introduced by D. Heldt et al. in the paper mentioned above served as a starting point for the research which is conducted in this thesis. A central aim of this work is to broaden the applicability of the AVI algorithm to additional areas in the oil and gas industry, like seismic imaging and the compact representation of unconventional geological structures. For this purpose several new algorithms are developed, among others the so-called Approximate Buchberger M{\"o}ller (ABM) algorithm and the Extended-ABM algorithm. The numerical aspects and the runtime of the methods are analysed in detail - based on a solid foundation of the underlying mathematical and algorithmic concepts that are also provided in this thesis. It is shown that the worst case runtime of the ABM algorithm is cubic in the number of input points, which is a significant improvement over the biquadratic worst case runtime of the AVI algorithm. Furthermore, we show that the ABM algorithm allows us to exercise more direct control over the essential properties of the computed approximate border basis than the AVI algorithm. The improved runtime and the additional control turn out to be the key enablers for the new industrial applications that are proposed here. As a conclusion to the work on the computation of approximate border bases, a detailed comparison between the approach in this thesis and some other state of the art algorithms is given. Furthermore, this work also addresses one important shortcoming of approximate border bases, namely that central concepts from exact algebra such as syzygies could so far not be translated to the setting of approximate border bases. One way to mitigate this problem is to construct a "close by" exact border bases for a given approximate one. Here we present and discuss two new algorithmic approaches that allow us to compute such close by exact border bases. In the first one, we establish a link between this task, referred to as the rational recovery problem, and the problem of simultaneously quasi-diagonalising a set of complex matrices. As simultaneous quasi-diagonalisation is not a standard topic in numerical linear algebra there are hardly any off-the-shelf algorithms and implementations available that are both fast and numerically adequate for our purposes. To bridge this gap we introduce and study a new algorithm that is based on a variant of the classical Jacobi eigenvalue algorithm, which also works for non-symmetric matrices. As a second solution of the rational recovery problem, we motivate and discuss how to compute a close by exact border basis via the minimisation of a sum of squares expression, that is formed from the polynomials in the given approximate border basis. Finally, several applications of the newly developed algorithms are presented. Those include production modelling of oil and gas fields, reconstruction of the subsurface velocities for simple subsurface geometries, the compact representation of unconventional oil and gas bodies via algebraic surfaces and the stable numerical approximation of the roots of zero-dimensional polynomial ideals.}, subject = {Computeralgebra}, language = {en} }