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      A problem-solving environment for the numerical solution of nonlinear algebraic equations

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      Ter-Thesis.pdf (1.464Mb)
      Date
      2007-03
      Author
      Ter, Thian-Peng
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      Nonlinear algebraic equations (NAEs) occur in many areas of science and engineering. The process of solving these NAEs is generally difficult, from finding a good initial guess that leads to a desired solution to deciding on convergence criteria for the approximate solution. In practice, Newton's method is the only robust general-purpose method for solving a system of NAEs. Many variants of Newton's method exist. However, it is generally impossible to know a priori which variant of Newton's method will be effective for a given problem.Many high-quality software libraries are available for the numerical solution of NAEs. However, the user usually has little control over many aspects of what the library does. For example, the user may not be able to easily switch between direct and indirect methods for the linear algebra. This thesis describes a problem-solving environment (PSE) called pythNon for studying the effects (e.g., performance) of different strategies for solving systems of NAEs. It provides the researcher, teacher, or student with a flexible environment for rapid prototyping and numerical experiments. In pythNon, users can directly influence the solution process on many levels, e.g., investigation of the effects of termination criteria and/or globalization strategies. In particular, to show the power, flexibility, and ease of use of the pythNon PSE, this thesis also describes the development of a novel forcing-term strategy for approximating the Newton direction efficiently in the pythNon PSE.
      Degree
      Master of Science (M.Sc.)
      Department
      Computer Science
      Program
      Computer Science
      Supervisor
      Spiteri, Raymond J.
      Committee
      Mould, David; Horsch, Michael C.; Szmigielski, Jacek
      Copyright Date
      March 2007
      URI
      http://hdl.handle.net/10388/etd-03262007-113126
      Subject
      nonlinear algebraic equations
      forcing-term strategies
      problem-solving environments
      Newton's method
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