A Class of Iterative Formulae for Solving Equations  

作　　者：Sheng Feng LI1,2,3, Jie Qing TAN1,2, Jin XIE1,2,4, Xing HUO1,2 1. School of Computer & Information, Hefei University of Technology, Anhui 230009, P. R. China 2. Institute of Applied Mathematics, Hefei University of Technology, Anhui 230009, P. R. China 3. Department of Mathematics & Physics, Bengbu College, Anhui 233030, P. R. China 4. Department of Mathematics & Physics, Hefei University, Anhui 230601, P. R. China 

出　　处：《Journal of Mathematical Research and Exposition》2010年第2期217-226,共10页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos.60773043;60473114);the Key Project Foundation of Scientific Research, Ministry of Education of China (Grant No.309017);the Doctoral Program Foundation of Ministry of Education of China (Grant No.20070359014);the Natural Science Key Foundation of Education Department of Anhui Province (Grant No.KJ2010A237);the Research Funds for Young Innovation Group of Education Department of Anhui Province (Grant No.2005TD03);the Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province (Grant No.2010SQRL118);the Research Funds for Young Teachers in the College of Education Department of Anhui Province (Grant No.2008jq1158)

摘　　要：Using the forms of Newton iterative function, the iterative function of Newton’s method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton’s method and Halley’s method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ（x） and μ（x）. Therefore, our iteration schemes are feasible and effective.Using the forms of Newton iterative function, the iterative function of Newton’s method to handle the problem of multiple roots and the Halley iterative function, we give a class of iterative formulae for solving equations in one variable in this paper and show that their convergence order is at least quadratic. At last we employ our methods to solve some non-linear equations and compare them with Newton’s method and Halley’s method. Numerical results show that our iteration schemes are convergent if we choose two suitable parametric functions λ（x） and μ（x）. Therefore, our iteration schemes are feasible and effective.

关 键 词：Non-linear equation iterative function order of convergence Newton＇s method Halley＇s method. 

分 类 号：O241.6[理学—计算数学]