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Dissertations / Theses on the topic 'Iterative methods (Mathematics)'

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Published: 4 June 2021

Last updated: 1 August 2024

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1

McKay, Melanie. "Iterative methods for incompressible flow." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28063.

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The goal of this thesis is to illustrate the effectiveness of iterative methods on the discretized Navier Stokes equations. The standard lid-driven cavity in both 2-D and 3-D test cases are examined and compared with published results of the same type. The numerical results are obtained by reducing the partial differential equations (PDEs) to a system of algebraic equations with a stabilized P1-P1 Finite Element Method (FEM) in space. Gear's Backward Difference Formula (BDF2) and an adaptive time stepping scheme utilizing a first order Backward Euler (BE) startup and BDF2 are then utilized to discretizc the time derivative of the Javier-Stokes equations. The iterative method used is the Generalized Minimal Residual (GMRES) along with the selected preconditioners Incomplete LU Factorization (ILU), Jacobi preconditioner and the Block Jacobi preconditioner.

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2

Kwan, Chun-kit, and 關進傑. "Fast iterative methods for image restoration." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224520.

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3

Karelius, Fanny. "Stationary iterative methods : Five methods and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69711.

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Systems of large sparse linear equations frequently arise in engineering and science. Therefore, there is a great need for methods that can solve these systems. In this thesis we will present three of the earliest and simplest iterative methods and also look at two more sophisticated methods. We will study their rate of convergence and illustrate them with examples.

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4

Kwan, Chun-kit. "Fast iterative methods for image restoration /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk:8888/cgi-bin/hkuto%5Ftoc%5Fpdf?B22956281.

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5

Ho, Ching-wah. "Iterative methods for the Robbins problem /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22054789.

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6

何正華 and Ching-wah Ho. "Iterative methods for the Robbins problem." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31222572.

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7

Sivaloganathan, S. "Iterative methods for large sparse systems of equations." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370302.

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8

Roberts, Harriet. "Preconditioned iterative methods on virtual shared memory machines." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-07292009-090522/.

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9

須成忠 and Cheng-zhong Xu. "Iterative methods for dynamic load balancing in multicomputers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233302.

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10

Xu, Cheng-zhong. "Iterative methods for dynamic load balancing in multicomputers /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13458905.

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11

Ho, Man-Kiu, and 何文翹. "Iterative methods for non-hermitian positive semi-definite systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30289403.

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12

Bängtsson, Erik. "Robust preconditioned iterative solution methods for large-scale nonsymmetric problems." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86353.

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We study robust, preconditioned, iterative solution methods for large-scale linear systems of equations, arising from different applications in geophysics and geotechnics. The first type of linear systems studied here, which are dense, arise from a boundary element type of discretization of crack propagation in brittle material. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems are nonsymmetric and indefinite and arise from finite element discretization of the partial differential equations describing the elastic part of glacial rebound processes. An equal order finite element discretization is analyzed and an optimal stabilization parameter is derived. The indefinite algebraic systems are of 2-by-2-block form, and therefore block preconditioners of block-factorized or block-triangular form are used when solving the indefinite algebraic system. There, the required Schur complement is approximated in various ways and the quality of these approximations is compared numerically. When the block preconditioners are constructed from incomplete factorizations of the diagonal blocks, the iterative scheme show a growth in iteration count with increasing problem size. This growth is stabilized by replacing the incomplete factors with an inner iterative scheme with a (nearly) optimal order multilevel preconditioner.

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13

Katsaggelos, Aggelos Konstantinos. "Constrained iterative image restoration algorithms." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/15830.

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14

Ambrus, Gergely Bezdek András. "Iterative processes generating dense point sets." Auburn, Ala., 2006. http://repo.lib.auburn.edu/EtdRoot/2006/SPRING/Mathematics_and_Statistics/Thesis/AMBRUS_GERGELY_20.pdf.

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15

Yao, Ning. "Iterative algorithms for channel estimation and equalization /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?ELEC%202005%20YAO.

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16

Li, Ching-Chang. "Use of iterative techniques for the rigid-viscoplastic finite element analysis." Ohio : Ohio University, 1986. http://www.ohiolink.edu/etd/view.cgi?ohiou1183139974.

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17

Reuter, Laurie Hodges. "Rendering and magnification of fractals using iterated function systems." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/8250.

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18

Ng, Kwok-po, and 吳國寶. "Fast iterative methods for solving Toeplitz and Toeplitz-like systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31210946.

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19

Ng, Kwok-po. "Fast iterative methods for solving Toeplitz and Toeplitz-like systems /." [Hong Kong] : University of Hong Kong, 1992. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13340372.

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20

Imberti, David M. "Methods for increasing domains of convergence in iterative linear system solvers." Thesis, Purdue University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3613148.

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In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the Fiedler reordering.

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21

McQuain, William D. "Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-09052009-040457/.

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22

Kei, Chun-Ling. "Efficient complexity reduction methods for short-frame iterative decoding /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?ELEC%202002%20KEI.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002.
Includes bibliographical references (leaves 86-91). Also available in electronic version. Access restricted to campus users.

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23

Zhang, Ping. "Iterative Methods for Computing Eigenvalues and Exponentials of Large Matrices." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/789.

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In this dissertation, we study iterative methods for computing eigenvalues and exponentials of large matrices. These types of computational problems arise in a large number of applications, including mathematical models in economics, physical and biological processes. Although numerical methods for computing eigenvalues and matrix exponentials have been well studied in the literature, there is a lack of analysis in inexact iterative methods for eigenvalue computation and certain variants of the Krylov subspace methods for approximating the matrix exponentials. In this work, we proposed an inexact inverse subspace iteration method that generalizes the inexact inverse iteration for computing multiple and clustered eigenvalues of a generalized eigenvalue problem. Compared with other methods, the inexact inverse subspace iteration method is generally more robust. Convergence analysis showed that the linear convergence rate of the exact case is preserved. The second part of the work is to present an inverse Lanczos method to approximate the product of a matrix exponential and a vector. This is proposed to allow use of larger time step in a time-propagation scheme for solving linear initial value problems. Error analysis is given for the inverse Lanczos method, the standard Lanczos method as well as the shift-and-invert Lanczos method. The analysis demonstrates different behaviors of these variants and helps in choosing which variant to use in practice.

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24

Zhao, Jun. "Analysis of finite element approximation and iterative methods for time-dependent Maxwell problems." Texas A&M University, 2002. http://hdl.handle.net/1969/582.

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25

Ali, Ali Hasan. "Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.

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26

Paul, Baldine-Brunel. "Video Compression based on iterated function systems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/13553.

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27

Galbraith, Steven Douglas. "Iterations of elliptic curves." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28620.

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28

King, James F. "Dimension characteristics for invariant measures." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28788.

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29

Massopust, Peter Robert. "Space curves generated by iterated function systems." Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/29339.

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30

Hardin, Douglas Patten. "Hyperbolic iterated function systems and applications." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/30864.

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31

Safoutin, Michael John. "A methodology for empirical measurement of iteration in engineering design processes /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/7111.

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32

Simonis, Joseph P. "A numerical study of globalizations of Newton-GMRES methods." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-103501.

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33

Shepherd, David. "Optimisation of iterative multi-user receivers using analytical tools /." View thesis entry in Australian Digital Theses Program, 2008. http://thesis.anu.edu.au/public/adt-ANU20081114.221408/index.html.

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34

Choi, Yan-yu. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37680948.

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35

Choi, Yan-yu, and 蔡欣榆. "Residual Julia sets of Newton's maps and Smale's problems on the efficiency of Newton's method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37680948.

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36

Maines, N. D. "Preconditioned iterative methods for the boundary element solution of a hypersingular integral equation." Thesis, University of Salford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308202.

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37

Ahmad, Ab Rahman bin. "The AGE iterative methods for solving large linear systems occurring in differential equations." Thesis, Loughborough University, 1993. https://dspace.lboro.ac.uk/2134/32905.

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The work presented in this thesis is wholly concerned with the Alternating Group Explicit (AGE) iterative methods for solving large linear systems occurring in solving Ordinary and Partial Differential Equations (ODEs and PDEs) using finite difference approximations.

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38

O'Neal, Jerome W. "The use of preconditioned iterative linear solvers in interior-point methods and related topics." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-06242005-162854/.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006.
Parker, R. Gary, Committee Member ; Shapiro, Alexander, Committee Member ; Nemirovski, Arkadi, Committee Member ; Green, William, Committee Member ; Monteiro, Renato, Committee Chair.

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39

Neuman, Arthur James III. "Regularization Methods for Ill-posed Problems." Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1273611079.

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40

Li, Ningzhi. "The convergence envelope for iterative estimation in SS-PARSE." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2008m/li.pdf.

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41

Pang, Hong Kui. "New numerical methods and analysis for Toeplitz matrices with financial applications." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2492157.

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42

Chidume, Chukwudi Soares de Souza Geraldo. "Iteration methods for approximation of solutions of nonlinear equations in Banach spaces." Auburn, Ala., 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SUMMER/Mathematics_and_Statistics/Dissertation/Chidume_Chukwudi_33.pdf.

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43

Bai, Xianglan. "Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919.

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44

Gauthier, Guy 1960. "Terminal iterative learning for cycle-to-cycle control of industrial processes." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115909.

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The objective of this thesis is to study a cycle-to-cycle control approach called Terminal Iterative Learning Control (TILC) and apply it to the process of plastic sheet heating in a thermoforming oven. Until now, adjustments to the oven heater temperature setpoints have been made manually by a human operator following a trial and error approach. This approach causes financial losses, because plastic sheets are wasted during the period of time when the adjustments are made at the beginning of a production run. Worse, the heater setpoints are subject to modification because of variation in the ambient temperature, which has an important impact on the sheet reheat process.
The TILC approach is analyzed by studying the closed-loop system in the discrete cycle domain through the use of the z-transform. The system, which has dynamic behaviour in the time domain, becomes a static linear mapping in the cycle domain. One can then apply on this equivalent system a traditional control approach, while considering that the system output is sampled once at the end of the cycle. On the other hand, from the standpoint of the real system, this control approach can be viewed as cycle-to-cycle control.
The stability and rate of convergence of the TILC algorithm can be analyzed through the location of the closed-loop system poles in the cycle domain. This analysis is relatively easy for a first-order TILC but becomes more complex for a higher-order TILC algorithm. The singular value decomposition (SVD) is used to simplify the convergence analysis while decoupling the system in the cycle domain. The SVD technique can be used to facilitate the design of higher-order TILC algorithms.
Internal Model Control (IMC) is another approach that can make the ILC design easier, because there is only one parameter per filter to adjust. The IMC technique has an interesting feature. In the case where the system is nominal, the closed-loop transfer function of the system is the same as the IMC filter's transfer function. Therefore, the adjustment of the filter parameter allows the designer to select the desired system response.
For industrial processes such as thermoforming ovens, it is important that the systems controlled by TILC algorithms are stable and have good performance. For thermoforming ovens, the terminal sheet temperature response must not be too oscillatory from cycle to cycle, since this may lead to high heater temperature setpoints. In the most serious case, high heater temperatures can cause the sheet to melt and spill on the heating elements at the bottom of the oven.
The performance aspect must not be neglected, since it is important to minimize the number of wasted plastic sheets, particularly at process startup. To avoid such waste of time and material, it is necessary that the TILC algorithm converge as quickly as possible. However, the robustness and performance objectives are conflicting and an acceptable compromise must be achieved. The control engineer must define specifications to describe these two constraints. Tools such as the Hinfinity Mixed-Sensitivity Analysis and mu-Analysis can be used to check the compliance of a given TILC algorithm with the robustness and performance specifications defined before the analysis. One can therefore compare various TILC algorithms quantitatively, through a computed measure obtained with one of the two approaches. These same tools can be used for the design of TILC algorithms, using weighting functions representing the specifications.
Simulation and experimental results obtained on industrial thermoforming machines show the effectiveness of the various approaches in this thesis. Many examples are also presented throughout the chapters.

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45

Snyder, Jason Edward Urbaʹnski Mariusz. "The global structure of iterated function systems." [Denton, Tex.] : University of North Texas, 2009. http://digital.library.unt.edu/permalink/meta-dc-9917.

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46

Yang, Tao Electrical Engineering &amp Telecommunications Faculty of Engineering UNSW. "Performance of iterative detection and decoding for MIMO-BICM systems." Awarded by:University of New South Wales. School of Electrical Engineering and Telecommunications, 2006. http://handle.unsw.edu.au/1959.4/26197.

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Multiple-input multiple-output (MIMO) wireless technology is an emerging cost- effective approach to offer multiple-fold capacity improvement relative to the conven- tional single-antenna systems. To achieve the capacities of MIMO channels, MIMO bit-interleaved-coded-modulation (BICM) systems with iterative detection and decod- ing (IDD) are studied in this thesis. The research for this dissertation is conducted based on the iterative receivers with convolutional codes and turbo codes. A variety of MIMO detectors, such as a maximum a posteriori probability (MAP) detector, a list sphere detector (LSD) and a parallel interference canceller (PIC) together with a decision statistic combiner (DSC), are studied. The performance of these iterative receivers is investigated via bounding techniques or Monte-Carlos simulations. Moreover, the computational complexities of the components are quantified and compared. The convergence behaviors of the iterative receivers are analyzed via variance trans- fer (VTR) functions and variance exchange graphs (VEGs). The analysis of conver- gence behavior facilitates the finding of components with good matching. For a fast fading channel, we show that the "waterfall region" of an iterative receiver can be predicted by VEG. For a slow fading channel, it is shown that the performance of an iterative receiver is essentially limited by the early interception ratio (ECR) which is obtained via simulations. After the transfer properties of the detectors are unveiled, a detection switching (DSW) methodology is proposed and the switching criterion based on cross entropy (CE) is derived. By employing DSW, the performance of an iterative receiver with a list sphere detector (LSD) of a small list size is considerably improved. It is shown that the iterative receiver achieves a performance very close to that with a maximum a posteriori probability (MAP) detector but with a significantly reduced complexity. For an iterative receiver with more than two components, various iteration sched- ules are explored. The schedules are applied in an iterative receiver with PIC-DSC. It is shown that the iterative receiver with a periodic scheduling outperforms that with the conventional scheduling at the same level of complexity.

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47

Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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48

Pornsawad, Pornsarp, and Christine Böckmann. "Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7083/.

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This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.

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49

Liu, Fang. "Numerical solutions of nonlinear elliptic problem using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/liuf/fangliu.pdf.

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50

Vines, Greg. "Signal modeling with iterated function systems." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/13315.

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