| A Class of Iterative Formulae for Solving Equations |
| Received:January 01, 2009 Revised:May 20, 2009 |
| Key Words:
Non-linear equation iterative function order of convergence Newton's method Halley's method.
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| Fund Project: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) and the Research Funds for Young Teachers in the College of Education Department of Anhui Province (Grant No.2008jq1158). |
| Author Name | Affiliation | | Sheng Feng LI | School of Computer & Information, Hefei University of Technology, Anhui 230009, P. R. China
Institute of Applied Mathematics, Hefei University of Technology, Anhui 230009, P. R. China
Department of Mathematics & Physics, Bengbu College, Anhui 233030, P. R. China | | Jie Qing TAN | School of Computer & Information, Hefei University of Technology, Anhui 230009, P. R. China
Institute of Applied Mathematics, Hefei University of Technology, Anhui 230009, P. R. China | | Jin XIE | School of Computer & Information, Hefei University of Technology, Anhui 230009, P. R. China
Institute of Applied Mathematics, Hefei University of Technology, Anhui 230009, P. R. China
Department of Mathematics & Physics, Hefei University, Anhui 230601, P. R. China | | Xing HUO | School of Computer & Information, Hefei University of Technology, Anhui 230009, P. R. China
Institute of Applied Mathematics, Hefei University of Technology, Anhui 230009, P. R. China |
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| Abstract: |
| 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 $\lambda (x)$ and $\mu (x)$. Therefore, our iteration schemes are feasible and effective. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.02.003 |
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