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| Chaos & fractals method for solving systems of nonlonear equations |
| Received:December 19, 2007 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20096015 |
| KeyWord:nonlinear equations chaos fractals newton iterative method global set of solutions |
| Author | Institution |
| 冯春 |
西南交通大学 物流学院,成都 |
| 张怡 |
西南交通大学 电气工程学院,成都 |
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| Abstract: |
| Chaos ＆ Fractals is a universal phenomenon. Newton-Raphson method is an important technique for calculating one dimensional or multi-dimensional variable, Newton-Raphson method is a nonlinear discrete dynamic process that exhibits sensitive dependence on initial guess point, which shows a fractal nature. the sensitive area of Newton-Raphson function is called the Julia set that is the boundaries of basins of attractions (solutions) display the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point optimization function and an optimization method to find Julia set point is proposed. A novel approach based on utilizing sensitive fractal areas to locate the Julia set point to find all the solutions of the nonlinear equations is proposed. The numerical simulation results show that the method is effective. |