| 摘要: |
| 通过分析常用的求解非线性问題的数值方法,提出一类具强烈几何背景的多点曲线法。多点曲线法不仅具有 超二次收敛的特性,而且避免了高阶导数,其收敛域比高阶非Newton法的收敛域有明显改善。数值算例结果表明多 点曲线法在奇异非线性方程和非线性方程组求解等问题中非常实用。 |
| 关键词: 非线性方程 高阶收敛性 非线性方程组 奇异性 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金项目(60971132) |
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| Multi-point curve method of solving nonlinear equation |
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YU Gui-jie1,U Wei-guo2
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(1. College of Transport & Storage and Civil Engineering in China University of Petroleum, Qingdao 266555, China ;2. College of Mathematics and Computational Sciences in China University of Petroleum, Dongying 257061， China)
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| Abstract: |
| By analyzing the traditional numerical methods of solving nonlinear equations，a kind of multi-point curve methods which have strong geometric background were presented. This kind of methods not only have super-quadratic convergence, but also can iterate without higher derivatives. Furthermore, the convergent fields of these new methods are obviously improved compared with higher order non-Newton method. The numerical results show that the presented method is effective in solving singular nonlinear equation and nonlinear systems of equations. |
| Key words: nonlinear equation higher order convergence nonlinear systems of equations singularity |
