2017-03-202017-03-08GUEVARA, Stefan Alberto Gómez. Unificando o análise local do método de Newton em variedades Riemannianas. 2017. 76 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2017.http://repositorio.bc.ufg.br/tede/handle/tede/6951In this work we consider the problem of finding a singularity of a field of differentiable vectors X on a Riemannian manifold. We present a local analysis of the convergence of Newton's method to find a singularity of field X on an increasing condition. The analysis shows a relationship between the major function and the vector field X. We also present a semi-local Kantorovich type analysis in the Riemannian context under a major condition. The two results allow to unify some previously unrelated results.application/pdfAcesso AbertoConvergência localConvergência semi-localFunção majoranteMétodo de NewtonVariedades RiemannianasLocal convergenceNewton's methodMajorant principleRiemannian manifoldSemi-local convergênceCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação