TY - JOUR T1 - An Acceleration Method in the Homotopy Newton's Continuation for Nonlinear Singular Problems AU - Yang , Zhong-Hua JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 6 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9492.html KW - AB -

The nonlinear singular problem $f(u)=0$ is considered. Here $f$ is a $C^3$ mapping from $E^n$ to $E^n$. The Jacobian matrix $f'(u)$ is singular at the solution $u^*$ of $f(u)=0$. A new acceleration method in the homotopy Newton's continuation is proposed. The quadratic convergence of the new algorithm is proved. A numerical example is given.