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

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.

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 not multi-step compared with known real polynomials by iterations. It is single - step but parabolic iterative methods.