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 vec...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.展开更多
基金suported in part by the National Natural Science Foundation of China(Grant No.10271025)Program for New Century Excellent Talents in University.
文摘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.
