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一族带积分信息的多点迭代函数

吴紫电   

  1. 上海交通大学
  • 出版日期:1983-04-14 发布日期:1983-04-14

吴紫电. 一族带积分信息的多点迭代函数[J]. 计算数学, 1983, 5(4): 398-402.

A FAMILY OF MULTIPOINT ITERATIVE FUNCTIONS WITH INTEGRAL INFORMATIONS

  1. Wu Zi-dian Shanghai Jiao-tong University
  • Online:1983-04-14 Published:1983-04-14
构造求解非线性纯量方程f(x)=0的迭代法,通常使用的信息是f(x)及其前s阶导数在若干点上的值,即所谓f(x)的标准信息集?_(m,f),如下表示:
A Family of multipoint iterative functions with integral informations are construct-ed in this paper. It is shown that the order of convergence for the iterative functionwhich requires 1 evaluaion of f and n-1 evaluations of integral informations is about5×(1+2~(1/2))~(n-3). The application of these iterations in practice is profitable if the eva-luation cost of the value of integral is approximately equal to the evaluation cost offunction or its derivatives.
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[1] H. T. Kung, J. F. Traub. Optimal Order of One-Point and Multipoint Iteration,J. ACM,21,4(1974) , 643--651.
[2] B. Kacewicz, An Integral-Interpolation Iterative Method for The Solution of Scalar Equations,Numer. Math., 26, 4(1976) ,355-365.
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