Fractal–Based Newton Method and Mechanism Synthesis & Approximate Synthesis

Abstract:

Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, utilizing a fractal iteration system to produce initial value, a new method to find all solutions of the nonlinear equations was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

• Periodical: Applied Mechanics and Materials (Volumes 155-156)
• Pages: 420-423
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.155-156.420
• Online since: February 2012
• Authors: You Xin Luo, Ling Fang Li
• Keywords: Fractals, Julia Set, Linkage Mechanism, Mandelbrot Set, Nonlinear Equations

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