A Significant Improvement on Newton’s Iterative Method
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摘要: 对解非线性和超越方程f(x)=0的牛顿迭代法作了重要的改进.利用动力系统的李雅普诺夫方法,构造了新的“牛顿类”方法.这些新的迭代方法保持了牛顿法的收敛速率和计算效能,摒弃了强加于f(x)的单调性要求f'(x)≠0.Abstract: For solving nonlinear and transcendental equation f(x)=0, a singnificant improvement on Newton s method is proposed in this paper. New Newton Like methods are founded on the basis of Liapunovs methods of dynamic system. These new methods preserve qudratic convergence and computation efficiency of Newtons method, but remove the monotoneity condition imposed on f(x):f(x)≠0.
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Key words:
- nonlinear equation /
- transcendental equation /
- dynamic system /
- iterative method /
- Newton method /
- numerical analysis
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[1] Hale J K.Ordinary Differential Equations[M].Huntington,New York:Robert E Krieger Publishing Company,1982. [2] Hirsch M W,Smale S.Differential Equations,Dynamic Systems and Linear Algebra[M].New York and London:Academic Press,1974,192~193. [3] 吴新元.解Stiff常微分方程的精确指数拟合法[J].南京大学学报(自然科学版),1997,31(1):1~6. [4] Traub J F.Solution of transcendental equations[A].In:A Ralston,H S Wilf Eds.Mathematical Methods for Digital Computers[C].Vol.New York:John Wiley & Sons,Inc,1968. -
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