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论文类型：期刊论文

发表时间：2013-01-01

发表刊物：ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS

收录刊物：SCIE、EI、Scopus

卷号：40

页面范围：373-380

ISSN号：1068-9613

关键字：Homotopy continuation; damped Newton method; domain of convergence; nonlinear algebraic equations; semilinear elliptic equations; finite element method

摘要：The homotopy continuation method and the damped Newton method are two known methods for circumventing the drawback of local convergence of the standard Newton method. Although some relations between these two methods have already been obtained, these relations are mainly for the differential equations which determine the paths followed by the two methods, rather than the sequences generated by the algorithms. In this paper, these sequences are investigated and some further relations are explored in terms of the marching directions and the step sizes during the iteration processes. Numerical solution of a semilinear elliptic equation is included to illustrate the relations discovered.