Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros
Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros
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DOI：
10.1109/tac.2008.2008345
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发表时间：
2009-01-01
影响因子：
6.8
通讯作者：
Zitek, Pavel
中科院分区：
文献类型：
--
作者：
Vyhlidal, Tomas;Zitek, Pavel
提出了一种计算滞后拟多项式在复平面上大范围内的所有零点的方法。该方法是基于映射的准多项式和利用零链的渐近性质。首先，根据拟多项式的分布图确定链的渐近指数。其次，大区域自由的零被定义。最后，零点被定位为准多项式的真实的和虚部的零级曲线的交点，其在无零点的区域之外的区域上被评估。
A method for computing all zeros of a retarded quasi-polynomial that are located in a large region of the complex plane is presented. The method is based on mapping the quasi-polynomial and on utilizing asymptotic properties of the chains of zeros. First, the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi-polynomial. Secondly, large regions free of zeros are defined. Finally, the zeros are located as the intersection points of the zero-level curves of the real and imaginary parts of the quasi-polynomial, which are evaluated over the areas of the region outside those free of zeros.