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Basin attractors for various methods |
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| Authors: | Melvin Scott Changbum Chun |
| Affiliation: | a 494 Carlton Court, Ocean Isle Beach, NC 28469, USA b Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, USA c Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea |
| 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. |
| Keywords: | Basin of attraction Iterative methods Simple roots Nonlinear equations |
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