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| 一种新的求非线性方程组的数值延拓法 | |
| 引用本文： | 郭俊,吴开腾,张莉,夏林林.一种新的求非线性方程组的数值延拓法[J].计算数学,2017,39(1):33-41. |
| 作者姓名： | 郭俊 吴开腾 张莉 夏林林 |
| 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, 内江 641112; 3. 重庆市巴川中学, 重庆 402569 |
| 基金项目： | 国家自然科学基金青年基金（11502121），四川省教育厅创新团队计划项目（13TD00001）和内江师范学院重点学科“计算数学”（0430101）资助. |
| 摘 要： | 针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题. |
| 关 键 词： | 同伦算法 Jacobi奇异问题 Newton法 数值延拓法 非线性方程组 |
A NEW CLASS OF NUMERICAL CONTINUATION METHOD FOR SOLVING THE NONLINEAR EQUATIONS |
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| Guo Jun,Wu Kaiteng,Zhang Li,Xia Linlin.A NEW CLASS OF NUMERICAL CONTINUATION METHOD FOR SOLVING THE NONLINEAR EQUATIONS[J].Mathematica Numerica Sinica,2017,39(1):33-41. | |
| Authors: | Guo Jun Wu Kaiteng Zhang Li Xia Linlin |
| Institution: | 1. College of Mathematics and Soft Science, Sichuan Normal University, Chengdu 610066, China; 2. Key Laboratory of Numerical Simulation in Sichuan Province, Neijiang Normal University, Neijiang 641100, China; 3. The Bachuan Middle School, Chongqing 402569, China |
| Abstract: | In order to solve the Jacobi singular problem in the process of the iteration,in this paper,a new numerical continuation method is proposed.The Jacobi singularity is overcome by constructing the double-parameter homotopy operator,using controlled conditions and selecting appropriate parameter,and the convergence of this method is analyzed.Finally,the feasibility and superiority of this method is validated by numerical comparison,especially with the advantages of crossing the Jacobi singular problem (points,lines,surfaces).Thus,to an extent,this method can also solve the problem of being heavily dependent on the initial value,which is the shortcoming of the numerical continuation method. |
| Keywords: | homotopy algorithm Jacobi singular problem Newton's method numerical continuation method system of nonlinear equations |
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