| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 6422058 | Applied Mathematics and Computation | 2011 | 16 Pages |
Abstract
There are many methods for the solution of a nonlinear algebraic equation. The methods are classified by the order, informational efficiency and efficiency index. Here we consider other criteria, namely the basin of attraction of the method and its dependence on the order. We discuss several methods of various orders and present the basin of attraction for several examples. It can be seen that not all higher order methods were created equal. Newton's, Halley's, Murakami's and Neta-Johnson's methods are consistently better than the others. In two of the examples Neta's 16th order scheme was also as good.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Melvin Scott, Beny Neta, Changbum Chun,