| 王礼广,杨竹莘,田泽荣.一种适合于求实系数多项式近似复根的迭代法[J].南华大学学报(自然科学版),2007,21(1):25~29.[.An Iterative Method Fit for Finding Complex Roots of Polynomials with Real Cefficients[J].Journal of University of South China(Science and Technology),2007,21(1):25~29.] |
| 一种适合于求实系数多项式近似复根的迭代法 |
| An Iterative Method Fit for Finding Complex Roots of Polynomials with Real Cefficients |
| 修订日期：2007-01-25 |
| DOI： |
| 中文关键词: 非线性方程,方程求根法,迭代法,牛顿法,实系数多项式的根 |
| 英文关键词:non-linear equation,finding roots of equations,iteration method,Newton method,roots of polynomials with real coefficients |
| 基金项目:湖南省教育厅科研资助项目(06C712) |
| 王礼广 杨竹莘 田泽荣 |
| 国防科学技术大学计算机学院，东北财经大学数量经济学院，湖南师范大学理学院 湖南长沙410073，南华大学数理学院，湖南衡阳421001，辽宁大连116025，湖南长沙410081 |
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| 中文摘要: |
| 提出了一种适合于求实系数多项式近似复根的迭代法,并进行了收敛性分析,给出了若干数值实例.该方法与切线牛顿法共同构架了复数域上求非线性代数方程近似解的基本方法.在切线牛顿法失效时它可替代使用.其收敛的阶为3,高于切线牛顿法的收敛阶2.特别地,与已有的抛物迭代法相比较,该方法是单步而非多步. |
| 英文摘要: |
| This paper proposes an iterative method fit for finding complex roots of polynomials with real coefficients,and carries on the analysis for its convergence,and shows some actual examples.This method and the tangent Newton method together construct the basic idea to find approximate roots of an algebraic equation in the complex number field,and it can take the place of the tangent Newton method when the later is failed.Its convergence order is 3,which is greater than 2,one of the tangent Newton method.Specially,it can calculate all real and complex roots of the real polynomials by iterations.It is single-step but not multi-step compared with known parabolic iterative methods. |
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