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首页> 外文期刊>Journal of Harbin Institute of Technology >Newton chaos iteration method and its application to mechanism kinematics synthesis
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Newton chaos iteration method and its application to mechanism kinematics synthesis

机译：牛顿混沌迭代法及其在机构运动学综合中的应用

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摘要

Many questions in natural science and engineering can be transformed into nonlinear equations. Newton iteration method is an important technique to one dimensional and multidimensional variables and iteration itself is very sensitive to initial guess point. This sensitive area is the Julia set of nonlinear discrete dynamic system which Newton iteration method forms. The Julia set, which is the boundaries of basins of attractions, displays the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point function and making use of inverse image iteration method, a method to find Julia set point was introduced. For the first time, a new method to find all solutions was proposed based on utilizing sensitive fractal areas to locate the Julia set points to find all solutions of the nonlinear questions. The developed technique used an important feature of fractals to preserve shape of basins of attraction on infinitely small scales. The numerical examples in linkage synthesis showed that the method was effective and correct.
机译：自然科学和工程学中的许多问题都可以转化为非线性方程。牛顿迭代法是处理一维和多维变量的重要技术，迭代本身对初始猜测点非常敏感。这个敏感区域是牛顿迭代法形成的非线性离散动力系统的Julia集。朱莉娅集（Julia set）是景点盆地的边界，显示出复杂的分形结构和混沌现象。通过构造排斥两周期点函数并利用逆图像迭代法，介绍了一种寻找朱莉娅设定点的方法。首次提出了一种新的求解所有问题的方法，即利用敏感的分形区域来定位Julia设定点，从而找到非线性问题的所有解决方案。所开发的技术利用分形的一个重要特征来在无限小的规模上保持吸引盆地的形状。连锁合成的数值算例表明该方法是有效和正确的。

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