(untitled) (Journal of Computational Mathematics, 2018)
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.