黎曼流形上奇异向量场的简单牛顿迭代法

The simple Newton's iteration of a singular vector field on Riemannian manifold

通过在黎曼流形上引入中心Lipschitz条件与Moore-Penrose广义逆,给出了为求黎曼流形上奇异向量场的零点的简单牛顿迭代法的收敛判别条件.对给定的初值p0若满足一定的条件,则以p0为初值的简单牛顿迭代所产生的点列收敛于奇异向量场的零点.

With the introduction of center Lipschitz condition and Moore-Penrose inverse on Riemannian manifold, the criterion of convergence of simple Newton＇s iteration for the singular vector field is given, that is, the sequence generated by simple Newton＇s iteration with initial point P0 converges to a zero of the singular vector field.