CONSTRUCTION OF ALGORITHMS

Author: BUSQUIER SÁEZ SONIA.
Year: 2003.
University: POLITÉCNICA DE CARTAGENA [www.upct.es].
Place of defense: INGENIEROS INDUSTRIALES.
Place of preparation: ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA INDUSTRIAL.

Summary: By studying a method iterarivo, one of the most important aspects to consider is the convergence (of the same order). For this analysis it is sometimes enough to know an interval [a, b] containing the root, the more certain scenario regularly, this kind of convergence is known as convergence global.Otros results ( "type Kantarovich"), provide sufficient conditions on him operator and the first approximation to the solution (pivot) to ensure that the succession by the scheme to converge a solution of the equation, leading to calls theorems semilicales of convergencia.Por Finally, in the so-called convergence theorems premises, assumptions are imposed on the entire root buscada.A other such toremas provide estimates error.Por another , the implementation and efficiency of the schemes are indispensable to estudiar.A this regard, the paper explores strategies to optimize such properties. Throughout this work suggests various methods (modifications Steffensen, blotting, Halley, etc.), considering its convergence (where widespread theorems for the classical methods), its implementation and its efficiency compared with the existing methods (where see their improvements). turn, proposes various theoretical methods for classics (interpretations and geometric theorems convergence).

Author: BERZAL FERNÁNDEZ JOSE ANDRES.
Year: 2003.
University: POLITÉCNICA DE MADRID [www.upm.es].
Place of defense: ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN.
Place of preparation: ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN.

Summary: The thesis develops three lines fundamental research into neural networks hebbianas. Initially, it conducts an analysis of the behavior patterns of Sanger Rubner and to characterize its dynamic evolution and stability. It was also proposed and evaluán some improvements in the design of the above models: some to optimize its calculation and others to expand their versatility and spectrum utilization. On the other hand, considers the appropriateness of the use of these networks hebbianas for the Principal Component Analysis and transform Karhunen-Loève and, in this sense been weighed the advantages of neural approach versus conventional procedures of implementation. From a computational point of view, it evaluates efficiency of these models in image compression applications static images and multispectral video sequences. Additionally, it implements a system for short-term prediction of meteorological parameters integrating different neural models, among which are networks hebbianas as a tool for preprocessing and reduced dimensionality. Finally, it outlines the implementabilidad hardware these models.

Author: GARCÍA RODRÍGUEZ JOSÉ ANTONIO.
Year: 2004.
University: MÁLAGA [www.uma.es].
Place of defense: FACULTAD DE CIENCIAS , UNIVERSIDAD DE MÁLAGA.
Place of preparation: SANTIAGO DE COMPOSTELA..

Summary: This report deals with the resolution of systems of equations kind of shallow waters in the case of a fluid as two capas.Se introduces a theoretical framework for the deduction of numerical schemes for problems with products not conservative and source terms and addresses the parallelization of the resulting algorithms. The first chapter takes place the deduction of the model type shallow waters of one two layers based on the Navier-Stokes 3D, and equations conducting a process of vertical integration and abolition of small terms. In chapter 2, which operates an extension of the methods of Roe to widespread problems 1D using the so-called method of líneas.Se Two results of consistency and good balanced schemes presentados.Por latest changes are proposed for the numerical scheme numerical resolve various difficulties associated with the resolution of the schemes obtained for the case of a fluid and two layers, such as the emergence of fronts wet and dry areas instabilities Kelvin-Helmholtz in the case of two layers of fluid . Due to alevado computational cost associated with the resolution of these equations due to the large magnitude of temporal and spatial scales at which they resolved, takes place parallelization of these algorithms using different paradigms of computing paralela.En Specifically, in chapter the third was carried out by the parallelization of using the same domain decomposition techniques and a cluster of PCs. Also set up a library in C + + that allows uasar the SSE multimedia instructions for performing operations with matrix arrays of small stature. Finally, in chapter 4, there are various numerical tests that have served to validate the numerical schemes introduced in chapter 2, being carried out comparisons with laboratory testing, and various applications to real problems (floods on the River Mero, in exchange bilayer the Strait of Gibraltar).

Author: HERRANZ SOTOCA JAVIER.
Year: 2004.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: SALA D'ACTES FME, EDIFICI U, CAMPUS SUD.
Place of preparation: U FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Author: DELGADO GRACIA JORGE.
Year: 2004.
University: ZARAGOZA [www.unizar.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: This memory can be framed within the computer-aided geometric design (CAGD). For the design can be done in an efficient manner is necessary for the curve or surface designed with a form suggested by your estate or network control, respectively, when a system satisfies these properties deaths say that preserves the way. Moreover, it is very important that the algorithms associated with such curves have desirable properties for the design, ie algorithms are cutting corners (these algorithms have very good properties for stability). The algorithm of Casteljau is cutting corners algorithm that is commonly used in CAGD to assess polynomial curves (curves represented on the basis of Bernstein, which preserves the way). Nevertheless, the algorithm of Casteljau has a computational complexity quadratic and literature have emerged lately algorithms cutting corners more efficient alternative to the algorithm of Casteljau. Thus, the thesis has conducted a study of the properties of preservation form the foundations associated with these algorithms. Specifically, it has analyzed the bases Said-Ball and Wang-Ball. The findings of this study showed that none of the alternate representations met at the same time the following properties: preserving the form and have an associated algorithm for evaluating cutting corners with computational complexity linear. This memory has obtained a satisfying both properties. Moreover, in the case of base Wang-Ball, algorithm complexity linear assessment, although not have good preservative properties of a standardized form for not being entirely positive, meets at least the preservation of monotony. Thus, whereas in general systems functions that can deduce an algorithm cutting corners there has been a theoretical study of the properties of such systems deforms preservation and the stability of the relevant algorithms. We tested these systems always meet the preservation of monotony. Also, a study has been made of the adaptation of different algorithms for curves considered the case of the evaluation of surfaces and the corresponding form of preservative properties of the surfaces. Finally, it has conducted a thorough analysis of error in the corresponding algorithms considered along memory.

Author: López Fernández María.
Year: 2005.
University: VALLADOLID [www.uva.es].
Place of defense: Fac.Ciencias, Univ.de Valladolid.
Place of preparation: Fac.de Ciencias, Univ.de Valladolid.

Summary: The thesis is divided into two parts. In the first part (Chapters 1 and 2), we developed a method to reverse efficient numerical Laplace transform under certain properties, what we call sectoral processed that are commonplace in the framework of the parabolic equations, but also listed other problems as in the treatment of certain conditions border transparent and computing various special functions. In essence, in Part I studied squaring for a comprehensive outline that appears in the formula for reversing a Laplace transform. In the second part of the thesis (Chapters 3 and 4), we believe discretizaciones of convolutions cored sectoral obtained by convolution of one paper-based methods Runge-Kutta and linear multipass methods, developed by Ch. Lubich (1988, 2004) and Ch. Lubich & A. Ostermann (1993). The objective of Part II is to develop efficient numerical methods to approximate the solutions generated by these about one of convolution. For example, in the context of PVI's linear parabolic, this translates into approximate discretization Runge-Kutta of the solution continuously original problem. The link to Part I is that the numerical methods we propose is based on the discretization of certain comprehensive outline ideas very similar to those which appear in the method of reversing the Laplace transform in Part I.

Author: HERMANNS MIGUEL.
Year: 2005.
University: POLITÉCNICA DE MADRID [www.upm.es].
Place of defense: ESCUELA TÉCNICAS SUPERIOR DE INGENIEROS AERONÁUTICOS.
Place of preparation: ESCUELA TÉCNICA SUPERIOR DE INGENIEROS AERONÁUTICOS.

Summary: The high-order numerical methods is characterized by the property that, as the number of nodes, or degrees of freedom, its error is much less than that of the second-order numerical methods. This makes them very attractive for applications such as noise and aeroacústica computational, predicting transition or direct numerical simulation dela turbulence. But the high-order numerical methods tend to be numerically unstable, which has hindered its widespread use. The origin of these instabilities is attributed to the presence of contours and the way in which the boundary conditions imposed on these methods. In the present work is achieved stability of numerical methods for high-order finite difference by inhibiting the phenomenon of Runge, head of the huge swings that were observed in the polynomial interpolation performed with nodes equiespaciados. Following the philosophy behind the Chebyshev polynomials, it introduces the idea of a mesh for optimal interpolation polynomial pieces to a lesser degree q N. It shows that when q = N, polynomial interpolation nodes on optimal interpolation coincides with the Chebyshev, and therefore schemes resulting finite difference methods are equivalent to the placement of Chebyshev. In the opposite limit, when q? No, it is shown that group with a few nodes, the order of O (q), is sufficient to achieve the desired stability of the numerical method. Through resolution numerical operators convección-difussión and acoustic shows that this new family of finite difference methods is able to obtain numerically stable solutions for any degree q? Ny that these solutions have a transitional correct behavior. That is why it has spread the use of these numerical methods to the study of two different problems fluidynamic combustion. In the first of these problems is studied local extinction and subsequent resignation of a call spread between two opposing currents of fuel and oxidizer that is disrupted by a whirlwind cancel. The local extinction of the flame leads to the emergence of two fronts flame separating the region extinct in the regions still active layer reactive mixture. The dynamics of these fronts flame is modeled using previous numerical results, which has retained the effects of releasing calo, and providing the speed of propagation of fronts ignition and extinction depending on the number of Dmak ohler locally. The temporal evolution of the mixed layer is described using a simplified analytical description of the velocity field of the fluid combined with the traditional approach of mixing fraction, which retain both the effects of non-stationary as the curvature. Although the effects of variable density play an important role in the layers of reactive mixture, the description of the layer of batter in the present work has been carried out assuming that the density is constant. The theoretical model developed shows what adimensionales relevant parameters that govern the interactions of eddies with flames media, and provides a range of values for these parameters for which the system is more interesting local extinction of the flame followed by his resignation Summary triple by flames. Despite the simplicity of the proposed model, the results that are obtained are consistent with the experimental results significantly published on interactions with eddies called diffusion. The second problem combustion studied is the vaporization p 8 osterior 7f7 combustion of fuel droplets immersed in a convective flow slow. In the limit of low numbers Peclet, Pe, convection associated with the velocity of the flow oxidizer incident is a first approximation negligible at distances of the order to drop the radio of the drop. Only in the region of Oseen, located at distances of the order / Pe, convection begins to be as prevalent as the spread. For hydrocarbons most common presenting a estequiometría overall S large compared to unity, the flame is located in this region if we consider the limit of distinguished Pe? 1 / S, which induces changes in order unity in the temperature and density, requiring the use of numerical techniques for describing the problem fluidodinámico result. Overall analysis of this problem of multiple scales is done by developments asintóticos trailers, where acomplamiento must take place between the solutions semianalíticas of the interior region and numerical solutions obtained in the region of Oseen. The analysis reveals what adimensionales relevant parameters in each region and shows that the existence of the flame significantly reduces the speed at which the airflow impact on the drop, thus changing their rate of vaporization and its resistance aerodynamics.

Author: Trillo Moya Juan Carlos.
Year: 2006.
University: VALENCIA [www.uv.es].
Place of defense: Facultad de Matemáticas. Universidad de Valencia..
Place of preparation: Facultad de Matemáticas.

Summary: In this thesis elaborates on the study of nonlinear patterns multirresolución within Harten. Emphasis is placed on applications of these schemes to digital image processing. In particular, it defines a new operator reconstruction, which leads to a pattern of subdivision and multirresolución nonlinear PPH (piecewise polynomial harmonic) with characteristics that make it very attractive for applications in image processing. It proves that the operator reconstruction PTT is well suited to the presence of discontinuities in the data. It also explores the preservative properties of the convexity of operators PPH reconstruction and subdivision. It applies to the PTT multirresolución scheme for compressing digital images and the results are quite promising. In addition to this fundamental line based on the new scheme PPH also includes two additional chapters in which it is implementing the unique value decomposition of a matrix for image compression and filling areas lost in a picture respectively . In the chapter that deals with the SVD. There is a decomposition algorithm combining that with the transformations multirresolución, and discusses the pros and cons of this strategy. The greatest contribution of the chapter is to provide an algorithm together with control of the error. In the last chapter devoted to filling in areas lost digital images designing a deterministic algorithm that performs the filling of the data either locally. Its main strength is the speed of execution.