| HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD |
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| 作者姓名： | References： |
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| 作者单位： | Liang Kewei Dept.of Math.，Zhejiang Univ.，Hangzhou 310027，China. |
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| 摘 要： | A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper.For every convergence theorem,a convergence ball is respectively introduced,where the hypothesis conditions of the corresponding theorem can be satisfied.Since all of these convergence balls have the same center x~*,they can be viewed as a homocentric ball. Convergence theorems are sorted by the different sizes of various radii of this homocentric ball, and the sorted sequence represents the degree of weakness on the conditions of convergence theorems.
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| 关 键 词： | 正交法 半局部收敛定理 局部收敛定理 牛顿法 |
| 文章编号： | 10.1007/s11766-007-0313-3 |
| 收稿时间： | 10 January 2007 |
| 修稿时间： | 2007-01-10 |
Homocentric convergence ball of the secant method |
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| Liang Kewei.HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD[J].Applied Mathematics A Journal of Chinese Universities,2007,22(3):353-365. |
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| Authors: | Liang Kewei |
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| Institution: | (1) Dept. of Math., Zhejiang Univ., Hangzhou, 310027, China |
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| Abstract: | A local convergence theorem and five semi-local convergence theorems of the secant method are listed in this paper. For every convergence theorem, a convergence ball is respectively introduced, where the hypothesis conditions of the corresponding theorem can be satisfied. Since all of these convergence balls have the same center x*, they can be viewed as a homocentric ball.Convergence theorems are sorted by the different sizes of various radii of this homocentric ball,and the sorted sequence represents the degree of weakness on the conditions of convergence theorems. |
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| Keywords: | secant method semi-local convergence theorem local convergence theorem convergence ball homocentric ball |
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