• 论文 •

求超越方程复根的圆等分点法

1. 大连工学院应用数学系
• 出版日期:1984-03-14 发布日期:1984-03-14

THE CIRCLE-EQUISECTING POINT METHOD FOR DETERMINING COMPLEX ZEROS OF A TRANSCENDENTAL EQUATION

1. Luo Yuan-quan Dalian Engineering Institute
• Online:1984-03-14 Published:1984-03-14
§1.问题的提出及基本定理 考虑下列超越方程: f(x)=0 (1)的求根问题。本文始终假定f(x)是p阶整函数,其中p是正整数。我们不要求x是实数时f(x)取实值,也不要求f(x)只有实零点。寻求方程(1)复根的问题,在理论上和应用上都是有意义的,因此引起了人们的兴趣。任给复数x_0,假定与x_0距离最近的根只有
The object of this paper is o propose method for determining the complex zeros of thetranscendental equation f(x)=0 without using derivatives. It is based on the following theo-rem: Assume that f(z) is a p th order entire function. Given two complex numbers x_0 andh,if f(z_1)=0, where |z_1-x>h|, and f(x)≠0 as x≠z_1∧|x-x_0|≤|z_1-x_0|,thenwhere i=(-1)~(1/2), and q is a positive integer.
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 [1] 罗远诠,解超越方程的三点迭代法,大连工学院学报,No.2,1982． [2] 罗远诠,求p阶整函数零点的一簇大范围收敛的迭代法,待发表. [3] 徐利治,朱自强,关于某些大范围收敛的迭代方法的评述,高等学校计算数学学报,No.2,1979,131-142． [4] H. W. Kuhn, Fixed-Points, Algorithms and Applications, Academic Press. Inc.. New York. 1977． [5] E.C.梯其玛希,函数论,科学出版社,1962．
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