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Thesis.pdf (13.79 MB)
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Zeros, Zeros, Zeros: How To Find Them Using Broyden's Method
Author Info
Sutherland, James
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu150305892468206
Abstract Details
Year and Degree
2017, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Abstract
Zero-finding methods are used in a wide variety of applications throughout computational mathematics. Newton's method is arguably the most well-known iterative zero-finding method, but its need of the Jacobian matrix in higher dimensions can sometimes lead to serious problems. In 1965, C.G. Broyden developed two n-dimensional secant methods that use the Jacobian only at the initial iterate and perform a rank-one update at all other iterations. Over time these methods became known as Broyden's ``good" method and Broyden's ``bad" method. There have been many studies done with a few carefully selected initial points that conclude the naming of Broyden's methods are accurate. However, rather than focusing on just a few isolated initial points, in this project convergence plots were utilized as a primary tool in the analysis of these methods to facilitate an investigation of several million initial points at once. Using a variety of examples involving nonlinear functions, the results show that each method has its benefits depending on the problem under investigation. The labels ``good" and ``bad" can be misleading and should not influence one method to be used more frequently than the other.
Committee
Edward Overman (Advisor)
Ching-Shan Chou (Committee Member)
Pages
103 p.
Subject Headings
Mathematics
Keywords
zero-finding
;
Broyden
;
convergence
;
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Citations
Sutherland, J. (2017).
Zeros, Zeros, Zeros: How To Find Them Using Broyden's Method
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu150305892468206
APA Style (7th edition)
Sutherland, James.
Zeros, Zeros, Zeros: How To Find Them Using Broyden's Method.
2017. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu150305892468206.
MLA Style (8th edition)
Sutherland, James. "Zeros, Zeros, Zeros: How To Find Them Using Broyden's Method." Master's thesis, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu150305892468206
Chicago Manual of Style (17th edition)
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Document number:
osu150305892468206
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2,328
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.