多项式零点的并行圆盘迭代法研究  

Study on Parallel Disc Iterative Method of Polynomial Zero

作　　者：努尔麦麦江·阿布都吾甫 Nuermaimaijiang Abuduwufu(School of Mathematics and Statistics,Kashi University,Kashi 844000,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000

出　　处：《宜春学院学报》2020年第9期32-36,共5页Journal of Yichun University

基　　金：喀什大学校级教改一般课题“线上线下混合教学模式的应用——以数学与应用数学专业教师教育课程为例”(KJDY1914)的研究成果。

摘　　要：本文在异步并行圆盘迭代法的基础上,为更快捷的求解多项式零点构建了一种新的圆盘迭代法,并在与异步并行圆盘迭代法相类似的条件下得到了它的收敛性定理。结果表明:该算法不仅保持原算法的优点,而且对于有重零点的多项式也适用。当n2,ξi∈W0=[x0;r0]是f(x)的一个mi重零点,而f(x)异于ξi外的其它零点都在中,如果α0<mi3则圆盘序列Wkk=0收敛于ξi,且rk+1rk32(miη0-r0)2。Based on the asynchronous parallel disk iterative method,a new disk iterative method is constructed for faster solution of polynomial zeros,and its convergence theorem is obtained under conditions similar to asynchronous parallel disk iterative methods.The results show that the algorithm not only maintains the advantages of the original algorithm,but also applies to polynomials with multiple zeros.Whenn2,ξi∈W0=[x0;r0]is a heavy zero point of f(x),and all other zeros other than are in,ifα0<mi3 then the disc sequence Wkk=0 converges toξi,and rk+1rk32(miη0-r0)2.

关 键 词：多项式 圆盘迭代法 重零点 收敛性定理 

分 类 号：O174[理学—数学]