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Convergence of the Newton method and uniqueness of zeros of vector fields on Riemannian manifolds. (English) Zbl 1116.53024
Summary: 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 Smale’s \(\gamma\)-theory are extended.

MSC:
53C20 Global Riemannian geometry, including pinching
65H10 Numerical computation of solutions to systems of equations
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