This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newton{like method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton's method.

[pt] Um modelo de previsão é uma ferramenta indispensável nos negócios, ajudando na tomada de decisões, seja a curto, médio ou longo prazo. Neste contexto, a implementação de técnicas de aprendizagem de máquina em modelos de previsão de séries temporais assume notória relevância, visto que o processamento da informação e a extração de conhecimento são cada vez mais exigidos de forma eficiente e dinâmica. Este trabalho desenvolve um modelo denominado Variable Step-Size evolving Participatory Learning with Kernel Recursive Least Squares, VS-ePL-KRLS, aplicado à previsão de preços do óleo diesel S500 e S10. O modelo apresentado demonstra uma melhor acurácia em comparação com os modelos análogos na literatura, sem perda de desempenho computacional para todas as séries temporais analisadas. / [en] A prediction model is an indispensable tool in business, helping to make decisions, whether in the short, medium, or long term. In this context, the implementation of machine learning techniques in time series forecasting models has a notorious relevance, as information processing and efficient and dynamic knowledge uncovering are increasingly demanded. This work develops a model called Variable Step-Size evolving Participatory Learning with Kernel Recursive Least Squares, VS-ePL-KRLS, applied to the forecast of weekly prices for S500 and S10 diesel oil, at the Brazilian level, for biweekly and monthly horizons. The presented model demonstrates a better accuracy compared with analogous models in the literature, without loss of computational performance for all time series analyzed.

Este trabalho apresenta um estudo sobre o método da continuação aplicado ao problema de fluxo de potência. Definições e conceitos de estabilidade de tensão são descritos de forma a explicitar as diferenças e semelhanças existentes com relação ao estudo de máximo carregamento em sistemas de energia elétrica. Uma síntese da teoria da bifurcação aborda sua importância em estudos de colapso de tensão. É proposta uma técnica de controle do tamanho do passo para o método da continuação com o objetivo de determinar o ponto de máximo carregamento (PMC) sem a necessidade de especificar, por meio do usuário, um valor para o tamanho inicial do passo. Os resultados dos estudos realizados em sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram a aplicação do método da continuação convencional e de sua associação à técnica de controle do tamanho do passo. / This work presents a research about the continuation method applied to the power flow problem. Voltage stability definitions and concepts are described in a way to highlight and point out the differences and the similarities among several methods used to determine the maximum loading of electrical power systems. A short description of the bifurcation theory is also presented in order to show its importance to the voltage collapse studies. A technique based on automatically controlling the step size is proposed as an innovation of the continuation method. The objective of this technique is to determine the maximum loading point without the traditional need of asking the user for the initial step size. The results compare the performance between the conventional and the new method. These methods are analyzed using IEEE test systems (14, 30, 57 and 118-bus).

Este trabalho apresenta um estudo sobre o método da continuação aplicado ao problema de fluxo de potência. Definições e conceitos de estabilidade de tensão são descritos de forma a explicitar as diferenças e semelhanças existentes com relação ao estudo de máximo carregamento em sistemas de energia elétrica. Uma síntese da teoria da bifurcação aborda sua importância em estudos de colapso de tensão. É proposta uma técnica de controle do tamanho do passo para o método da continuação com o objetivo de determinar o ponto de máximo carregamento (PMC) sem a necessidade de especificar, por meio do usuário, um valor para o tamanho inicial do passo. Os resultados dos estudos realizados em sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram a aplicação do método da continuação convencional e de sua associação à técnica de controle do tamanho do passo. / This work presents a research about the continuation method applied to the power flow problem. Voltage stability definitions and concepts are described in a way to highlight and point out the differences and the similarities among several methods used to determine the maximum loading of electrical power systems. A short description of the bifurcation theory is also presented in order to show its importance to the voltage collapse studies. A technique based on automatically controlling the step size is proposed as an innovation of the continuation method. The objective of this technique is to determine the maximum loading point without the traditional need of asking the user for the initial step size. The results compare the performance between the conventional and the new method. These methods are analyzed using IEEE test systems (14, 30, 57 and 118-bus).

Pour réaliser des simulations précises aux temps longs pour des vagues non linéaires, il faut faire appel à des algorithmes d’évolution temporelle précis. En particulier, la combinaison d’un pas de temps adaptatif avec un facteur intégrant est connue pour être très efficace. Nous proposons une modification de cette technique. Le principe consiste à soustraire un certain polynôme à une EDP. Puis, comme pour le facteur intégrant, nous faisons un changement de variable pour retirer la partie linéaire. Mais nous espérons retirer quelque chose de plus afin de rendre l’EDP moins raide pour les calculs numériques. Le polynôme choisi est une expansion de Taylor autour du temps initial de la solution. Afin de calculer les différentes dérivées nécessaires, nous utilisons le Dense Output qui donne la possibilité d’approximer les dérivées de la solution à tout temps. Une fois le facteur intégrant modifié appliqué, nous faisons appel à une avance temporelle classique afin de résoudre l’équation d’évolution. Il a été considéré plusieurs schémas de Runge-Kutta avec pas de temps adaptatif. Nous avons tiré avantage des méthodes emboîtées, afin de ne pas calculer de nouvelles fonctions et perdre du temps de calcul, en utilisant uniquement des données déjà calculées durant l’évolution temporelle. Les résultats numériques montrent que l’efficacité de notre méthode varie selon les cas. Par exemple, nous avons vérifié que plus le profil de l’onde est pentue, plus notre méthode est efficace. Pour le modèle de vagues non linéaires le plus compliqué à notre disposition, le modèle HOS, nous avons pu réduire le nombre de pas de temps de calcul jusqu’à près de 30 % avec un schéma de Runge-Kutta de Dormand-Prince et jusqu’à plus de 99 % pour un schéma de Bogacki-Shampine. / Efficient time stepping algorithms are crucial for accurate long time simulations of nonlinear waves. In particular, adaptive time stepping combined with an integrating factor are known to be very effective. We propose a modification of the existing technique. The trick consists in subtracting a certain-order polynomial to a PDE. Then, like for the integrating factor, a change of variables is performed to remove the linear part. But, here, we hope to remove something more to make the PDE less stiff to numerical resolution. The polynomial is chosen as a Taylor expansion around the initial time of the solution. In order to calculate the different derivatives, we use a dense output which gives a possibility to approximate the derivatives of the solution at any time. The modified integrating factor being applied, a classical time-stepping method can be used to solve the remaining equation. We focus on various Runge-Kutta schemes with a varying step size. We take advantage of embedded methods and use an evolved adaptive step control. We do not need to calculate new functions and loose time of calculation only by using already estimated values during the temporal evolution. Numerical tests show that the actual efficiency of the method varies along cases. For example, we verified that steeper waves profiles give rise to better behaviour of the method. For fully nonlinear water wave simulations with the HOS model, we can save up to 30% of total time steps with a Dormand-Prince Runge-Kutta scheme and we can save up to 99% with the Bogacki-Shampine scheme.

Tato práce je psaná v angličtině a je zaměřená na problematiku ekvalizace v digitálních komunikačních systémech. Teoretická část zahrnuje stručné pozorování různých způsobů návrhu ekvalizérů. Praktická část se zabývá implementací nejčastěji používaných ekvalizérů a s jejich adaptačními algoritmy. Cílem praktické části je porovnat jejich charakteristiky a odhalit činitele, které ovlivňují kvalitu ekvalizace. V rámci problematiky ekvalizace jsou prozkoumány tři typy ekvalizérů. Lineární ekvalizér, ekvalizér se zpětnou vazbou a ML (Maximum likelihood) ekvalizér. Každý ekvalizér byl testován na modelu, který simuloval reálnou přenosovou soustavu s komplexním zkreslením, která je složena z útlumu, mezisymbolové interference a aditivního šumu. Na základě implenentace byli určeny charakteristiky ekvalizérů a stanoveno že optimální výkon má ML ekvalizér. Adaptační algoritmy hrají významnou roli ve výkonnosti všech zmíněných ekvalizérů. V práci je nastudována skupina stochastických algoritmů jako algoritmus nejmenších čtverců(LMS), Normalizovaný LMS, Variable step-size LMS a algoritmus RLS jako zástupce deterministického přístupu. Bylo zjištěno, že RLS konverguje mnohem rychleji, než algoritmy založené na LMS. Byly nastudovány činitele, které ovlivnili výkon popisovaných algoritmů. Jedním z důležitých činitelů, který ovlivňuje rychlost konvergence a stabilitu algoritmů LMS je parametr velikosti kroku. Dalším velmi důležitým faktorem je výběr trénovací sekvence. Bylo zjištěno, že velkou nevýhodou algoritmů založených na LMS v porovnání s RLS algoritmy je, že kvalita ekvalizace je velmi závislá na spektrální výkonové hustotě a a trénovací sekvenci.

The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.