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Analyzing Domain Of Convergence For Broyden’S Method, Michael Bonthron
Analyzing Domain Of Convergence For Broyden’S Method, Michael Bonthron
College of Science and Health Theses and Dissertations
Broyden’s method is a quasi-Newton iterative method used to find roots of non-linear systems of equations. Research has shown and improved the rate of convergence for special cases and specific applications of the method. However, there is limited literature regarding the well-posedness of the method. In practice, a numerical method must reliably converge to the appropriate root. This paper will discuss the domain of attraction for the roots of a system found by using Broyden’s method. A method of approximating the radius of convergence of a root will be described which considers the largest disk centered at the root such …