Study of Newton Method on singularity of Vector Fields

In this talk we discuss the convergence rate of the Newton method for finding the singularity point on vetor fields. It is well-known that the Newton Method has local quadratic convergence rate with nonsingularity and Lipschitz condition. Here we release Lipschitz condition. With only nonsingularity, the Newton Method has superlinear convergence. If we have enough time, we can quickly give the damped Newton method on finding singularity on vector fields with superlinear convergence under nonsingularity condition only.