一种新的求非线性方程组的数值延拓法  

A NEW CLASS OF NUMERICAL CONTINUATION METHOD FOR SOLVING THE NONLINEAR EQUATIONS

作　　者：郭俊[1] 吴开腾[2] 张莉[2] 夏林林 

机构地区：[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

出　　处：《计算数学》2017年第1期33-41,共9页Mathematica Numerica Sinica

基　　金：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);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.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.

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 

分 类 号：O241.7[理学—计算数学]