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| 大范围求解非线性方程组的指数同伦法 | |
| 引用本文： | 夏林林,吴开腾.大范围求解非线性方程组的指数同伦法[J].计算数学,2014,36(2):215-224. |
| 作者姓名： | 夏林林 吴开腾 |
| 作者单位： | 1. 四川师范大学数学与软件科学学院, 成都 610066; 2. 内江师范学院四川省高等学校数值仿真重点实验室, 四川内江 641112 |
| 基金项目： | 四川省教育厅创新团队计划项目（13TD00001）. |
| 摘 要： | 为了解决关于奇异的非线性方程组求根问题,提出了一种由同伦算法推出大范围收敛的连续型方法-指数同伦法,构造了一类指数同伦方程,克服了Jacobi矩阵的奇异,分析了指数同伦方 |
| 关 键 词： | 指数同伦法 同伦算法 存在性 收敛性 |
| 收稿时间： | 2013-08-29; |
AN EXPONENTIAL HOMOTOPY METHOD FOR NONLINEAR EQUATIONS IN LARGE SCOPE |
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| Xia Linlin,Wu Kaiteng.AN EXPONENTIAL HOMOTOPY METHOD FOR NONLINEAR EQUATIONS IN LARGE SCOPE[J].Mathematica Numerica Sinica,2014,36(2):215-224. | |
| Authors: | Xia Linlin Wu Kaiteng |
| Institution: | 1. College of Mathematics and Soft Science, Sichuan Normal University, Chengdu, Sichuan 610066, China; 2. Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University, Neijiang, Sichuan 641100, China |
| Abstract: | In order to solve singular nonlinear equations, exponential homotopy method is proposed using the homotopy method, which is a continuous method with large-scale convergence. A class of exponential homotopy equations is established for modifying the singularities of Jacobian matrices. The solution of existence and convergence are analyzed. Finally, some numerical results are given to demonstrate the feasibility and validity of the exponential homotopy method. |
| Keywords: | Exponential homotopy method homotopy method existence convergence |
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