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Dissertations / Theses on the topic 'Linear equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.

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This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.

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2

Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,<br>This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term

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3

Goedhart, Eva Govinda. "Explicit bounds for linear difference equations /." Electronic thesis, 2005. http://etd.wfu.edu/theses/available/etd-05102005-222845/.

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4

Jonklass, Raymond. "Learners' strategies for solving linear equations." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52915.

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Thesis (MEd)--University of Stellenbosch, 2002.<br>ENGLISH ABSTRACT: Algebra deals amongst others with the relationship between variables. It differs from Arithmetic amongst others as there is not always a numerical solution to the problem. An algebraic expression can even be the solution to the problem in Algebra. The variables found in Algebra are often represented by letters such as X, y, etc. Equations are an integral part of Algebra. To solve an equation, the value of an unknown must be determined so that the left hand side of the equation is equal to the right hand side. There ar

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5

Altassan, Alaa Abdullah. "Linear equations over free Lie algebras." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/linear-equations-over-free-liealgebras(6e29b286-1869-4207-b054-8baab98e70df).html.

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In this thesis, we study equations of the form $[x_1,u_1]+[x_2, u_2]+\ldots+[x_k,u_k]=0$ over a free Lie algebra $L$, where $k>1$ and the coefficients $u_1, u_2, \ldots,u_k$ belong to $L$. The starting point of this research is a paper [22], in which the authors embarked on a systematic study of very concrete linear equations over free Lie algebras. They focused on the given equations in the case where $k=2$. We generalise and develop a number of the results on equations with two variables to equations with an arbitrary number of indeterminates. Most of the results refer to the case where the

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6

Chen, Hua, Wei-Xi Li, and Chao-Jiang Xu. "Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3028/.

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7

Hafez, Salah Taha. "Continued fractions and solutions of linear and non-linear lattice equations." Thesis, University of Kent, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236725.

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8

Torshage, Axel. "Linear Functional Equations and Convergence of Iterates." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-56450.

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The subject of this work is functional equations with direction towards linear functional equations. The .rst part describes function sets where iterates of the functions converge to a .xed point. In the second part the convergence property is used to provide solutions to linear functional equations by de.ning solutions as in.nite sums. Furthermore, this work contains some transforms to linear form, examples of functions that belong to di¤erent classes and corresponding linear functional equations. We use Mathematica to generate solutions and solve itera- tively equations.

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9

Grey, David John. "Parallel solution of power system linear equations." Thesis, Durham University, 1995. http://etheses.dur.ac.uk/5429/.

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At the heart of many power system computations lies the solution of a large sparse set of linear equations. These equations arise from the modelling of the network and are the cause of a computational bottleneck in power system analysis applications. Efficient sequential techniques have been developed to solve these equations but the solution is still too slow for applications such as real-time dynamic simulation and on-line security analysis. Parallel computing techniques have been explored in the attempt to find faster solutions but the methods developed to date have not efficiently exploite

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10

Serna, Rodrigo. "Solving Linear Systems of Equations in Hardware." Thesis, KTH, Skolan för elektro- och systemteknik (EES), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-200610.

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11

PEI, HUILING. "EXPLORING BOOTSTRAP APPLICATIONS TO LINEAR STRUCTURAL EQUATIONS." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1021928281.

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12

Jimenez, Amelia. "Hands-on equations program: An approach to teaching linear equations using manipulatives." Scholarly Commons, 2011. https://scholarlycommons.pacific.edu/uop_etds/94.

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Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been known to challenge students to think abstractly. This has become a difficult task for educators to accomplish. The challenge of teaching algebra becomes apparent when students do not comprehend the abstract reasoning of algebra. Many students need hel

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13

Fan, Ka-wing. "Prime solutions in arithmetic progressions of some quadratic equations and linear equations /." Hong Kong : University of HOng Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23540308.

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14

Dimakos, Michail. "Linear, linearisable and integrable nonlinear PDEs." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607875.

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15

Porter, Annabelle Louise. "The evolution of equation-solving: Linear, quadratic, and cubic." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3069.

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This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.

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16

Johnson, Solomon Nathan. "Best simultaneous approximation in normed linear spaces." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/58985.

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In this thesis we consider the problem of simultaneously approximating elements of a set B C X by a single element of a set K C X. This type of a problem arises when the element to be approximated is not known precisely but is known to belong to a set.Thus, best simultaneous approximation is a natural generalization of best approximation which has been studied extensively. The theory of best simultaneous approximation has been studied by many authors, see for example [4], [8], [25], [28], [26] and [12] to name but a few.

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17

De, Villiers Magdaline. "Existence theory for linear vibration models of elastic bodies." Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-10072009-201522.

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18

Le, Gia Quoc Thong. "Approximation of linear partial differential equations on spheres." Texas A&M University, 2003. http://hdl.handle.net/1969.1/22.

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The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both

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19

Benner, Peter, Enrique Quintana-Ortí, and Gregorio Quintana-Ortí. "Solving Linear Matrix Equations via Rational Iterative Schemes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601460.

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We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and perf

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20

Hendriks, Peter Anne. "Algebraic aspects of linear differential and difference equations." [S.l. : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1996. http://irs.ub.rug.nl/ppn/153769580.

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21

Becker, Dulcenéia. "Parallel unstructured solvers for linear partial differential equations." Thesis, Cranfield University, 2006. http://hdl.handle.net/1826/4140.

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This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation

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22

Qi, Yuan-Wei. "The blow-up of quasi-linear parabolic equations." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253381.

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23

Davidson, Bryan Duncan. "Recursive projection for semi-linear partial differential equations." Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294932.

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24

Caramanis, Constantine (Constantine Michael) 1977. "Solving linear partial differential equations via semidefinite optimization." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8949.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.<br>Includes bibliographical references (p. 49-51).<br>Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this thesis a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on both linear and nonlinear functionals defined on solutions of linear partial differential equations. We apply the proposed methods to examples of PDEs in one and two dimensions with very encouraging result

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25

van, Heerden Francois A. "Nonlinear Schrödinger Type Equations with Asymptotically Linear Terms." DigitalCommons@USU, 2002. https://digitalcommons.usu.edu/etd/7089.

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We study the nonlinear Schrödinger type equation - Δu + (λg(x) + l)u = f(u) on the whole space R^N. The nonlinearity f is assumed to be asymptotically linear and g(x) ≥ 0 has a potential well. We do not assume a limit for g(x) as lxl →∞ . Using variational techniques, we prove the existence of a positive solution for λ large. In the case where f is odd we obtain multiple pairs of solutions. The limiting behavior of solutions as λ →∞ is also considered.

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26

Palitta, Davide <1990&gt. "Numerical solution of large-scale linear matrix equations." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8342/1/tesi_completa2.pdf.

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We are interested in the numerical solution of large-scale linear matrix equations. In particular, due to their occurrence in many applications, we study the so-called Sylvester and Lyapunov equations. A characteristic aspect of the large-scale setting is that although data are sparse, the solution is in general dense so that storing it may be unfeasible. Therefore, it is necessary that the solution allows for a memory-saving approximation that can be cheaply stored. An extensive literature treats the case of the aforementioned equations with low-rank right-hand side. This ass

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27

Saravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods." Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-sp

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28

Mathia, Karl. "Solutions of linear equations and a class of nonlinear equations using recurrent neural networks." PDXScholar, 1996. https://pdxscholar.library.pdx.edu/open_access_etds/1355.

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Artificial neural networks are computational paradigms which are inspired by biological neural networks (the human brain). Recurrent neural networks (RNNs) are characterized by neuron connections which include feedback paths. This dissertation uses the dynamics of RNN architectures for solving linear and certain nonlinear equations. Neural network with linear dynamics (variants of the well-known Hopfield network) are used to solve systems of linear equations, where the network structure is adapted to match properties of the linear system in question. Nonlinear equations inturn are solved using

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29

Zhang, Junchi. "GPU computing of Heat Equations." Digital WPI, 2015. https://digitalcommons.wpi.edu/etd-theses/515.

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There is an increasing amount of evidence in scientific research and industrial engineering indicating that the graphic processing unit (GPU) has a higher efficiency and a stronger ability over CPUs to process certain computations. The heat equation is one of the most well-known partial differential equations with well-developed theories, and application in engineering. Thus, we chose in this report to use the heat equation to numerically solve for the heat distributions at different time points using both GPU and CPU programs. The heat equation with three different boundary conditions (Dirich

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30

Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and A

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31

Spence, Euan Alastair. "Boundary value problems for linear elliptic PDEs." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609476.

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32

Duelli, Markus Michael. "Functional calculus for bisectorial operators and applications to linear and non-linear evolution equations /." Berlin : Logos-Verl, 2005. http://deposit.ddb.de/cgi-bin/dokserv?id=2619697&prov=M&dok_var=1&dok_ext=htm.

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33

Torres, Ledesma César Enrique. "Non linear ellipter equations with non-local regional operators." Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/115927.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática<br>Esta tesis consiste de cinco partes. En la primera parte se considera el problema de Dirichlet lineal y no lineal con una difusi\'on no local regional definido implicitamente por \!\!donde $0< \alpha < 1$, $\rho \in C(\overline)$ y $\lambda dist(x,\partial \Omega) \leq \rho (x) \leq dist(x, \partial \Omega)$ con $\lambda \in (0,1]$, $x\in \Omega$. Haciendo uso del teorema de Lax-Milgran y el Teorema del paso de la monta\~na se demuestra la existencia de soluciones d\'ebiles. En la segunda parte, se considera la ecuaci\'on

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34

Nabti, Abderrazak. "Non linear, non-local evolution equations : theory and application." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS032.

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Cette thèse concerne l’étude qualitative (existence locale, existence globale, explosion en temps fini) de quelques équations de Schrödinger non-linéaires non-locales. Dans le cas où les solutions explosent en temps fini, l’estimation du temps maximal d’existence des solutions sera présentée. Le chapitre 1 concerne l’étude d’une équation de Schrödinger non-linéaire sur RN. On s’intéresse à l’existence locale d’une solution pour toute condition initiale donnée dans L2(RN). De plus, on montre que la norme-L2 de la solution explose en temps fini T < 1. Les démonstrations reposent essentielleme

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35

Roidot, Kristelle. "Numerical study of non-linear dispersive partial differential equations." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00692445.

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Numerical analysis becomes a powerful resource in the study of partial differential equations (PDEs), allowing to illustrate existing theorems and find conjectures. By using sophisticated methods, questions which seem inaccessible before, like rapid oscillations or blow-up of solutions can be addressed in an approached way. Rapid oscillations in solutions are observed in dispersive PDEs without dissipation where solutions of the corresponding PDEs without dispersion present shocks. To solve numerically these oscillations, the use of efficient methods without using artificial numerical dissipat

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36

Knight, Christopher J. K. "Freonts in non-linear wave equations with spatial inhomogeneity." Thesis, University of Surrey, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.549460.

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37

Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently lar

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38

Smith, James A. "“Looking for nothing" : Bayes linear methods for solving equations." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/2207/.

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Here I will describe and implement Bayes linear methods for finding zeros of deterministic functions. We assume that the zero is known to be unique. Initially, the value of the function is modelled simply as the product of two independent factors, the position of the point from the zero and a "slope" which is assumed to vary "smoothly” with position. Additional prior information specifies first and second order properties of the slopes and the position of the zero: in particular, smoothness is specified by modelling the slope process to be stationary with a decreasing correlation function. Thi

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39

Sproule, Olive Elizabeth. "The development of concepts of linear and quadratic equations." Thesis, Queen's University Belfast, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314224.

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40

Lee, Sang-Gu. "Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings." DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6984.

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We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = Xr1 + Xr2 + ... + Xrt and r1>r2>...>rt≥2. In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We also extended the

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41

Kisela, Tomáš. "Basics of Qualitative Theory of Linear Fractional Difference Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-234025.

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Tato doktorská práce se zabývá zlomkovým kalkulem na diskrétních množinách, přesněji v rámci takzvaného (q,h)-kalkulu a jeho speciálního případu h-kalkulu. Nejprve jsou položeny základy teorie lineárních zlomkových diferenčních rovnic v (q,h)-kalkulu. Jsou diskutovány některé jejich základní vlastnosti, jako např. existence, jednoznačnost a struktura řešení, a je zavedena diskrétní analogie Mittag-Lefflerovy funkce jako vlastní funkce operátoru zlomkové diference. Dále je v rámci h-kalkulu provedena kvalitativní analýza skalární a vektorové testovací zlomkové diferenční rovnice. Výsledky analý

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42

Tzou, Leo. "Linear and nonlinear analysis and applications to mathematical physics /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5761.

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43

Person, Axelle. "Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order." Rennes 1, 2002. http://www.theses.fr/2002REN1A007.

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44

Noble, Raymond Keith. "Some problems associated with linear differential operators." Thesis, Cardiff University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238160.

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45

Ang, W. T. "Some crack problems in linear elasticity /." Title page, table of contents and summary only, 1987. http://web4.library.adelaide.edu.au/theses/09PH/09pha581.pdf.

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46

Leccese, Andrew J. "Stability of parametrically forced linear systems /." Online version of thesis, 1994. http://hdl.handle.net/1850/11789.

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47

Sauer-Budge, Alexander M. (Alexander Michael) 1972. "Computing upper and lower bounds on linear functional outputs from linear coercive partial differential equations." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/30014.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2003.<br>Includes bibliographical references (p. 115-123).<br>Uncertainty about the reliability of numerical approximations frequently undermines the utility of field simulations in the engineering design process: simulations are often not trusted because they lack reliable feedback on accuracy, or are more costly than needed because they are performed with greater fidelity than necessary in an attempt to bolster trust. In addition to devitalized confidence, numerical uncertainty often causes ambigui

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48

Akkineni, Dharma Teja. "A Fourier Spectral Method to Solve Linear and Non-Linear Differential Equations and its Applications." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1418994964.

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49

Allen, Patrick. "Multiplicities of Linear Recurrence Sequences." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2942.

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In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and a result due to Brindza, Pintér and Schmidt. We then investigate ternary recurrences and exhibit a result due to Beukers building on work of Beukers and Tijdeman. The last two chapters deal with a very important result due to Schmidt in which we bound the zero-multiplicity of a linear recurrence sequence of order <em>t</em> by a function involving <em>t</em> alo

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50

馮漢國 and Hon-kwok Fung. "Some linear preserver problems in system theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B3121227X.

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