Date of Award
Master of Science (MS)
In the past, the use of higher order iterative methods for solving a system of nonlinear equations has been avoided because of the difficulties encountered in the evaluation of higher derivatives. With the aid of FEED (Fast and Efficient Evaluation of Derivatives), which is an automatic evaluation of derivatives, this paper compares a third order iterative method, Halley's method, with the standard (second order) iterative method, namely Newton's method. Comparisons are made with respect to three factors : 1) speed of convergence measured in terms of the number of iterations leading to convergence; 2) speed of convergence measured in terms of the total amount of work involved, where the amount of work is computed as the product of the number of iterations leading to convergence and the time periteration required; and 3) the size of the region of convergence. Halley's method gives larger regions of convergence near the roots, encounters fewer matrix singularities in solving the system and requires fewer iterations in achieving convergence. However, starting from initial guesses where both methods lead to convergence, Newton's method generally requires less computational work.
Chiu, Edwin K., "A Comparison Between Halley's Method and Newton's Method for Solving Systems of Nonlinear Equations Using Automatic Derivatives Evaluations" (1987). Archived Theses. 174.