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  Partner: UNT Libraries
 Department: Department of Mathematics
 Degree Level: Master's
 Collection: UNT Theses and Dissertations
A Comparative Study of Non Linear Conjugate Gradient Methods

A Comparative Study of Non Linear Conjugate Gradient Methods

Date: August 2013
Creator: Pathak, Subrat
Description: We study the development of nonlinear conjugate gradient methods, Fletcher Reeves (FR) and Polak Ribiere (PR). FR extends the linear conjugate gradient method to nonlinear functions by incorporating two changes, for the step length αk a line search is performed and replacing the residual, rk (rk=b-Axk) by the gradient of the nonlinear objective function. The PR method is equivalent to FR method for exact line searches and when the underlying quadratic function is strongly convex. The PR method is basically a variant of FR and primarily differs from it in the choice of the parameter βk. On applying the nonlinear Rosenbrock function to the MATLAB code for the FR and the PR algorithms we observe that the performance of PR method (k=29) is far better than the FR method (k=42). But, we observe that when the MATLAB codes are applied to general nonlinear functions, specifically functions whose minimum is a large negative number not close to zero and the iterates too are large values far off from zero the PR algorithm does not perform well. This problem with the PR method persists even if we run the PR algorithm for more iterations or with an initial guess closer to the ...
Contributing Partner: UNT Libraries
On Groups of Positive Type

On Groups of Positive Type

Date: August 1995
Creator: Moore, Monty L.
Description: We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.
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Polish Spaces and Analytic Sets

Polish Spaces and Analytic Sets

Date: August 1997
Creator: Muller, Kimberly (Kimberly Orisja)
Description: A Polish space is a separable topological space that can be metrized by means of a complete metric. A subset A of a Polish space X is analytic if there is a Polish space Z and a continuous function f : Z —> X such that f(Z)= A. After proving that each uncountable Polish space contains a non-Borel analytic subset we conclude that there exists a universally measurable non-Borel set.
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Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
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Regular Semigroups

Regular Semigroups

Date: August 1967
Creator: Penn, Howard L.
Description: This thesis describes semigroups and the properties of both regular and inverse semigroups.
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Borel Sets and Baire Functions

Borel Sets and Baire Functions

Date: January 1970
Creator: Wemple, Fred W.
Description: This paper examines the relationship between Borel sets and Baire functions.
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Connectedness and Some Concepts Related to Connectedness of a Topological Space

Connectedness and Some Concepts Related to Connectedness of a Topological Space

Date: August 1969
Creator: Wallace, Michael A.
Description: The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.
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Linear Algebras

Linear Algebras

Date: August 1961
Creator: Smith, Nickie Lee
Description: This paper is primarily concerned with the fundamental properties of a linear algebra of finite order over a field. A discussion of linear sets of finite order over a field is used as an introduction to these properties.
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A Classification of Regular Planar Graphs

A Classification of Regular Planar Graphs

Date: December 1972
Creator: McCalla, Linda F.
Description: The purpose of this paper is the investigation and classification of regular planar graphs. The motive behind this investigation was a desire to better understand those properties which allow a graph to be represented in the plane in such a manner that no two edges cross except perhaps at vertices.
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Continuous Multifunctions

Continuous Multifunctions

Date: August 1972
Creator: Rulon, Susan Ree
Description: This paper is a discussion of multifunctions, various types of continuity defined on multifunctions, and implications of continuity for the range and domain sets of the multifunctions.
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