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Dissertations / Theses on the topic 'Gauss-Seidel'
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1
Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-051305-162036/unrestricted/simonis.pdf.
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Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Digital WPI, 2005. https://digitalcommons.wpi.edu/etd-dissertations/285.
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Newton-Picard methods are iterative methods that work well for computing roots of nonlinear equations within a continuation framework. This project presents one of these methods and includes the results of a computation involving the Brusselator problem performed by an implementation of the method. This work was done in collaboration with Andrew Salinger at Sandia National Laboratories.
3
Wu, Wei. "Paving the Randomized Gauss-Seidel." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1074.
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The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix A and its column submatrices. The analysis demonstrates that RBGS improves RGS more when given appropriate column-paving of the matrix, a partition of the columns into well-conditioned blocks. The main result yields a RBGS method that is more e cient than the simple RGS method.
4
Liang, Yunxu. "Improved Gauss-Seidel iterative method on power networks." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008140.
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Hocking, Laird Robert. "A complex analysis based derivation of multigrid smoothing factors of lexicographic Gauss-Seidel." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/37012.
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This thesis aims to present a unified framework for deriving analytical formulas for multigrid smoothing factors in arbitrary dimensions, under certain simplifying assumptions. To derive these expressions we rely on complex analysis and geometric considerations, using the maximum modulus principle and Mobius transformations.
We restrict our attention to pointwise and block lexicographic Gauss-Seidel smoothers on a d-dimensional uniform mesh, where the computational molecule of the associated discrete operator forms a 2d+1 point star. In the pointwise case the effect of a relaxation parameter, as well as different choices of mesh ratio, are analyzed. The results apply to any number of spatial dimensions, and are applicable to high-dimensional versions of a few common model problems with constant coefficients, including the Poisson and anisotropic diffusion equations as well as the convection-diffusion equation. We show that in most cases our formulas, exact under the simplifying assumptions of Local Fourier Analysis, form tight upper bounds for the asymptotic convergence of geometric multigrid in practice. We also show that there are asymmetric cases where lexicographic Gauss-Seidel smoothing outperforms red-black Gauss-Seidel smoothing; this occurs for certain model convection-diffusion equations with high mesh Reynolds numbers.
6
Parks, Michael Lawrence. "Efficient Numeric Computation of a Phase Diagram in Biased Diffusion of Two Species." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/32896.
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A lattice gas with equal numbers of oppositely charged particles, diffusing under the influence of a uniform electric field and an excluded volume condition undergoes an order-disorder phase transition, controlled by the particle density and the field strength. This transition may be continuous (second order) or continuous (first order). Results from previous discrete simulations are shown, and a theoretical continuum model is developed. As this is a nonequilibrium system, there is no associated free energy to determine the location of a first order transition. Instead, the model equations for this system are evolved in time numerically, and the locus of this transition is determined via the presence of a stable state with coexisting regions of order and disorder. The Crank-Nicholson, nonlinear Gauss-Seidel, and GMRES algorithms used to solve the model equations are discussed. Performance enhancements and limits on convergence are considered.<br>Master of Science
7
Bokka, Naveen. "Comparison of Power Flow Algorithms for inclusion in On-line Power Systems Operation Tools." ScholarWorks@UNO, 2010. http://scholarworks.uno.edu/td/1237.
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The goal of this thesis is to develop a new, fast, adaptive load flow algorithm that "automatically alternates" numerical methods including Newton-Raphson method, Gauss-Seidel method and Gauss method for a load flow run to achieve less run time. Unlike the proposed method, the traditional load flow analysis uses only one numerical method at a time. This adaptive algorithm performs all the computation for finding the bus voltage angles and magnitudes, real and reactive powers for the given generation and load values, while keeping track of the proximity to convergence of a solution. This work focuses on finding the algorithm that uses multiple numerical techniques, rather than investigating programming techniques and programming languages. The convergence time is compared with those from using each of the numerical techniques. The proposed method is implemented on the IEEE 39-bus system with different contingencies and the solutions obtained are verified with PowerWorld Simulator, a commercial software for load flow analysis.
8
Tazeroualti, Mohammed. "Modélisation de surfaces à l'aide de fonctions splines : conception d'un verre progressif." Grenoble 1, 1993. http://tel.archives-ouvertes.fr/tel-00343495.
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Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide
9
Anderson, Curtis James. "Estimating the Optimal Extrapolation Parameter for Extrapolated Iterative Methods When Solving Sequences of Linear Systems." University of Akron / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1383826559.
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Jurča, Ondřej. "Ustálený chod a zkratové poměry v síti 110 kV E.ON napájené z rozvodny 110 kV Otrokovice v roce 2011." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-219016.
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Distribution network 110 kV owned by E. ON in the area Otrokovice; powered by 110 kV and two variants of involvement contained.The first option is basic involvement, without the use of the bridge. The second option includes involvement with the bridge. The aim of this study is to compare; by calculating the steady-state network operation and short circuit conditions of the network, the involvement of these two options. The thesis is divided into two parts, theoretical and practical. The theoretical part consists of a description of the steady operation of networks of high-voltage and short circuit ratio calculations. Load flow calculations are described by the Gauss-Seidel and Newton iterative method. In the case of short-circuit conditions, the effects of their characteristic values, processes and various methods of calculation are described.In the second part, this theoretical knowledge is applied to input data and dispatching programme with the appropriate calculations of network operation and short circuit conditions. The calculated values are listed in the thesis, on the basis of which an evaluation of the two possible connections is made.
11
Wang, Da. "Accelerated granular matter simulation." Doctoral thesis, Umeå universitet, Institutionen för fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-110164.
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Modeling and simulation of granular matter has important applications in both natural science and industry. One widely used method is the discrete element method (DEM). It can be used for simulating granular matter in the gaseous, liquid as well as solid regime whereas alternative methods are in general applicable to only one. Discrete element analysis of large systems is, however, limited by long computational time. A number of solutions to radically improve the computational efficiency of DEM simulations are developed and analysed. These include treating the material as a nonsmooth dynamical system and methods for reducing the computational effort for solving the complementarity problem that arise from implicit treatment of the contact laws. This allow for large time-step integration and ultimately more and faster simulation studies or analysis of more complex systems. Acceleration methods that can reduce the computational complexity and degrees of freedom have been invented. These solutions are investigated in numerical experiments, validated using experimental data and applied for design exploration of iron ore pelletising systems.<br><p>This work has been generously supported by Algoryx Simulation, LKAB (dnr 223-</p><p>2442-09), Umeå University and VINNOVA (2014-01901).</p>
12
Coskun, Korhan. "Three Dimensional Laminar Compressible Navier Stokes Solver For Internal Rocket Flow Applications." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12609086/index.pdf.
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A three dimensional, Navier-Stokes finite volume flow solver which uses Roe&rsquo<br>s upwind flux differencing scheme for spatial and Runge-Kutta explicit multi-stage time stepping scheme and implicit Lower-Upper Symmetric Gauss Seidel (LU-SGS) iteration scheme for temporal discretization on unstructured and hybrid meshes is developed for steady rocket internal viscous flow applications. The spatial accuracy of the solver can be selected as first or second order. Second order accuracy is achieved by piecewise linear reconstruction. Gradients of flow variables required for piecewise linear reconstruction are calculated with both Green-Gauss and Least-Squares approaches.
The solver developed is first verified against the three-dimensional viscous laminar flow over flat plate. Then the implicit time stepping algorithms are compared against two rocket motor internal flow problems. Although the solver is intended for internal flows, a test case involving flow over an airfoil is also given. As the last test case, supersonic vortex flow between concentric circular arcs is selected.
13
Marquez, Damian Jose Ignacio. "Multilevel acceleration of neutron transport calculations." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19731.
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Thesis (M.S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Stacey, Weston M.; Committee Co-Chair: de Oliveira, Cassiano R.E.; Committee Member: Hertel, Nolan; Committee Member: van Rooijen, Wilfred F.G.
14
Hoang, Thi Minh Phuong. "Optimisation des temps de calculs dans le domaine de la simulation par éléments discrets pour des applications ferroviaires." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2011. http://tel.archives-ouvertes.fr/tel-00726199.
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La dégradation géométrique de la voie ballastée sous circulation commerciale nécessite des opérations de maintenance fréquentes et onéreuses. La caractérisation du comportement des procédés de maintenance comme le bourrage, la stabilisation dynamique, est nécessaire pour proposer des améliorations en terme de méthode, paramétrage pour augmenter la pérennité des travaux. La simulation numérique d'une portion de voie soumise à un bourrage ou une stabilisation dynamique permet de comprendre les phénomènes physiques mis en jeu dans le ballast. Toutefois, la complexité numérique de ce problème concernant l'étude de systèmes à très grand nombre de grains et en temps de sollicitation long, demande donc une attention particulière pour une résolution à moindre coût. L'objectif de cette thèse est de développer un outil de calcul numérique performant qui permet de réaliser des calculs dédiés à ce grand problème granulaire moins consommateur en temps. La méthodologie utilisée ici se base sur l'approche Non Smooth Contact Dynamics (NSCD) avec une discrétisation par Éléments Discrets (DEM). Dans ce cadre, une méthode de décomposition de domaine (DDM) alliée à une parallélisation adaptée en environnement à mémoire partagée utilisant OpenMP sont appliquées pour améliorer l'efficacité de la simulation numérique.
15
"A comparison of Jacobi and Gauss-Seidel parallel iterations." Massachusetts Institute of Technology, Laboratory for Information and Decision Systems], 1988. http://hdl.handle.net/1721.1/3104.
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Chiang, Peiyu, and 江佩諭. "Initial Estimation for Distributed Gauss-Seidel Iteration Routing Algorithm." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/67204854420934086882.
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碩士<br>國立中正大學<br>資訊工程研究所<br>99<br>We can describe the problem of routing load balancing as a sort of partial differential equations(PDEs) from macroscopic perspective in wireless sensor network, we use of finite difference method to find the approximation solution of PDEs which can be formulated by linear equations solved by Gauss-Seidel Iteration, finally we will acquire the load balancing routing path.
Gauss-Seidel algorithm is a practical way in solving linear systems, not only the speed of solving procedure, but also the accuracy of the evaluation. But it cannot converge in the scenario which node density is varied a lot, although De la Garza Iteration method guarantee the convergent by took more iteration. So we’d like to design a simple initial value to deduct the converge iterations appropriately by Gauss-Seidel Iteration and De la Garza Iteration method, and the simple initial value will applied in more algorithms.
17
Csenki, Attila. "Rotations in the Plane and Prolog." 2007. http://hdl.handle.net/10454/3916.
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No<br>Rotation is a well-known operation on lists. We define its two-dimensional analogue and discuss its implementation in Prolog using difference lists. An application to the iterative solution of a system of linear equations by the Gauss¿Seidel method is given.
18
Wen, Huang Ching, and 黃靜文. "Gauss-Seidel Method and its Improving Versions for Solving H-matrices Linear Systems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/48974875007070889998.
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碩士<br>輔仁大學<br>數學系研究所<br>96<br>Solving linear system with H-matrix appeared in many applications and is studied by many numerical calculation researchers. In this thesis we first introduced some algorithms to judge the H-matrix. Then we applied the Gauss-Seidel method and its improving versions, MGS and IMGS, to solve such linear systems and systems with their corresponding comparison matrices. Both theoretical and numerical experiments have shown that the modified methods yield considerable improvement in the convergence rate, especially the IMGS method
with suitable parameter α.
19
Huang, Chunchieh, and 黃俊傑. "To Increase Parallelism Of Distributed Gauss-Seidel Routing Algorithm For Wireless Sensor Networks." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/53739501589661282328.
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碩士<br>國立中正大學<br>資訊工程研究所<br>100<br>In massive-dense Wireless Sensor Network (WSN), routing paths can be
considered as continuous lines. We could re-describe WSN by macroscopic
parameters, defining macroscopic models of geographic space to replace traditional
graphic models, and then it can avoid the complicated details produced by large
number of nodes. In macroscopic models, the routing problem of load balance can
described as a sort of partial differential equations (PDEs), after transforming it into
linear equations by use of finite difference method (FDM). The routing problem now
is transformed into solve this equations, and we can solve it by Gauss-Seidel iteration
method (GSI) which solutions is routing direction in WSN.
However, GSI cannot converge in some special WSN which node density varies
significantly. De la Garza Iteration method (DLGI) can solve this problem, but it needs
considerable rounds. Thus we design Color-Grouping Method to increase parallelism
of these algorithms, which method group grid points which updates in same round
according to property of distance, and this method will do iteration in grouping order,
it can substantially reduce the number of convergence rounds of GSI and DLGI.
20
Chu, Yu-Jun, and 屈羽濬. "Variable Step-Size Improved Gauss-Seidel Pseudo Proportionate Affine Projection Algorithm for Acoustic Echo Cancellation." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/746bp4.
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碩士<br>國立臺北科技大學<br>電機工程系研究所<br>99<br>Acoustic echo usually arises when sound from a loudspeaker is picked up by the microphone in the same room. In this thesis, two acoustic echo cancellation algorithms are proposed to anticipate the sound signal and cancel it out in order to improve the voice quality on a telephone call. The first one is the variable step size improved proportionate affine projection (VSS-IPAP) algorithm, and the second one is the variable step size improved Gauss-Seidel pseudo proportionate affine projection (VSS-IGSPPAP) algorithm. Four pseudo room space environments are simulated by different sparseness room impulse responses (RIR) in the experiment. The relative system distance (SD) and echo return loss enhancement (ERLE) are often used as the measure criteria to compare different acoustic echo cancellation algorithms. The experimental results show that both proposed algorithms are able to achieve superior performance than the well-known normalized least-mean-square (NLMS) algorithm and other traditional acoustic echo cancellation algorithms. However, like the affine projection (AP) algorithm, the VSS-IPAP algorithm always suffers a large amount of computational load. On the contrary, the proposed VSS-IGSPPAP algorithm not only provides fast convergence speed in different sparseness room impulse response (RIR) situations but also consumes low computational cost.
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Carter, Jerry W. "Implementation of a Lower-Upper Symmetric Gauss-Seidel Implicit Scheme for a Navier-Stokes Flow Solver." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-8020.
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The field of Computational Fluid Dynamics (CFD) is in a continual state of advancement due to new numerical techniques, optimization of existing codes, and the increase in memory and processing speeds of computers. In this thesis, the solution technique for a pre-existing Navier-Stokes flow solver is adapted from an explicit Runge Kutta method to a Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit time integration method. Explicit time integration methods were originally used in CFD codes because these methods require less memory. Information needed to advance the flow in time is localized to each grid point. These explicit methods are, however, restricted by time step sizes due to stability criteria. In contrast, implicit methods are unaffected by a large time step sizes but are restricted by memory requirements due to the complexities of unstructured grids. The implementation of LU-SGS performs grid re-ordering for unstructured meshes because of the coupling of grid points in the integration method's solution. The explicit and implicit flow solvers were tested for inviscid flows in incompressible, compressible, and transoinc flow regimes. The results found by comparing the implicit and explicit algorithms revealed a significant speed up in convergence to steady state by the LU-SGS method in terms of iteration number and CPU time per iteration.
22
Chiang, Yi, and 江懿. "A Prioritized Gauss-Seidel Method for Dense Correspondence Estimation and Motion Segmentation in Crowded Urban Areas with a Moving Depth Camera." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/40104611508341776709.
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碩士<br>國立臺灣大學<br>資訊工程學研究所<br>102<br>Dense RGB-D video motion segmentation is an important preprocessing module in computer vision, image processing and robotics. A motion segmentation algorithm based on an optimization framework which utilizes depth information only is presented in this thesis. The proposed optimization framework segments and estimates rigid motion parameters of each locally rigid moving objects with coherent motion. The proposed method also calculates dense point correspondences while performing segmentation. An efficient numerical algorithm based on Constrained Block Nonlinear Gauss-Seidel (CNLGS) algorithm [1] and Prioritized Step Search [2] is proposed to solve the optimization problem. It classifies variables including point correspondences into groups and determines the ordering of variables to optimize. We prove the proposed numerical algorithm to converge to a theoretical
bound. The proposed algorithm works well with a moving camera in highly dynamic urban scenes with non-rigid moving objects.
23
Nicolai, Andreas. "Co-Simulations-Masteralgorithmen - Analyse und Details der Implementierung am Beispiel des Masterprogramms MASTERSIM." 2018. https://tud.qucosa.de/id/qucosa%3A31973.
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In der Version 2.0 des Simulationskopplungsstandards FMI (Functional Mockup Interface) wird die Möglichkeit zur Speicherung und Wiederherstellung einer Simulationseinheit/FMU (Functional Mockup Unit) definiert. Dieses ist eine elementare Voraussetzung für iterierende Co-Simulations-Masteralgorithmen, wie z.B. Gauss-Seidel oder Newton-Iteration. Für die gekoppelte Simulation von solchen Simulationseinheiten ist ein Co-Simulations-Master erforderlich.
Das Simulationsmasterprogramm MASTERSIM ist ein solcher Co-Simulations-Master und enthält zahlreiche Algorithmen und eine effiziente Verwaltung von Simulationseinheiten unter Verwendung dieser neuen Schnittstellenfunktionen. Dieser Artikel dokumentiert grundlegende Co-Simulations-Algorithmen und beteiligte Parameter und illustriert deren Einfluss anhand eines Testbeispiels.:1. Grundlagen
2. Zeitintegration
3. Simulationsperformance
4. Testbeispiel
5. Kopplungsalgorithmen
6. Zusammenfassung
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Segunda, António Fernando. "Métodos para a resolução de sistemas de equações lineares." Master's thesis, 2018. http://hdl.handle.net/10400.6/10055.
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O objectivo deste trabalho é o de apresentar vários métodos numéricos que nos permitem obter
soluções aproximadas para sistemas de equações lineares. Os métodos de Jacobi e de Gauss-Seidel
são deduzidos, as condições de convergência apresentadas. São apresentados alguns exemplos de
aplicação e as soluções aproximadas são comparadas com a solução exacta.<br>The aim of this work is to present sereval numerical methods that allow us to obtain approximate
solutions to systems of linear equations. Jacobi and Gauss-Seidel methods are deduced and their
convergence conditions presented. Two examples of application are presented and the approximate
solutions are compared with the exact solution.
25
Tazeroualti, Mahammed. "Modélisation de surfaces à l'aide de fonctions splines :." Phd thesis, 1993. http://tel.archives-ouvertes.fr/tel-00343495.
Full textAbstract:
Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide