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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (8): 924-927.

• 论文 • 上一篇    下一篇

A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD

吴新元   

  1. Department of Mathematics, Nanjing University, Nanjing 210093, P R China
  • 收稿日期:1997-04-14 修回日期:1999-01-05 出版日期:1999-08-18 发布日期:1999-08-18

A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD

Wu Xinyuan   

  1. Department of Mathematics, Nanjing University, Nanjing 210093, P R China
  • Received:1997-04-14 Revised:1999-01-05 Online:1999-08-18 Published:1999-08-18

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摘要： 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 Liapunov’s methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton’s method, and remove the monotoneity condition imposed on f(x):f′(x)≠0.

关键词: nonlinear equation, transcendental equation, dynamic system, iterative method, Newton’s method, numerical analysis

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 Liapunov’s methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton’s method, and remove the monotoneity condition imposed on f(x):f′(x)≠0.

Key words: nonlinear equation, transcendental equation, dynamic system, iterative method, Newton’s method, numerical analysis

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