# A Problem-Solving Environment for the Numerical Solution of Nonlinear Algebraic Equations

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.

Advisor:Szmigielski, Jacek; Horsch, Michael C.; Mould, David; Spiteri, Raymond J.

School:University of Saskatchewan

School Location:Canada - Saskatchewan

Source Type:Master's Thesis

Keywords:nonlinear algebraic equations forcing term strategies problem solving environments newton s method

ISBN:

Date of Publication:03/26/2007