Convergence of the Newton method and uniqueness of zeros of vector fields on Riemannian manifolds
Convergence of the Newton method and uniqueness of zeros of vector fields on Riemannian manifolds
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DOI：
10.1360/04ys0147
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发表时间：
2005-11
影响因子：
1.4
通讯作者：
J. Li
中科院分区：
文献类型：
--
作者：
J. Li
在黎曼流形上向量场的协变导数满足一般Lipschitz条件的前提下，给出了向量场的牛顿法收敛球和零点唯一球的半径估计。推广了一些经典结果，如Kantorovich的类型定理和Smale的γ理论。
The estimates of the radii of convergence balls of the Newton method and uniqueness balls of zeroes of vector fields on the Riemannian manifolds are given under the assumption that the covariant derivatives of the vector fields satisfy some kind of general Lipschitz conditions. Some classical results such as the Kantorovich's type theorem and the Smale's γ -theory are extended.