| A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD |
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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.
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| 关 键 词： | nonlinear equation transcendental equation dynamic system iterative method Newton’s method numerical analysis |
| 收稿时间： | 1997-04-14 |
A significant improvement on Newton's interative method |
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| Wu Xinyuan. A significant improvement on Newton's interative method[J]. Applied Mathematics and Mechanics(English Edition), 1999, 20(8): 924-927. DOI: 10.1007/BF02452492 |
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| Authors: | Wu Xinyuan |
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| Affiliation: | (1) Department of Mathematics, Nanjing University, 210093 Nanjing, P R China |
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| 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 |
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| Keywords: | nonlinear equation transcendental equation dynamic system iterative method Newton's method numerical analysis |
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