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A modification of the classic conditions of Newton-Kantorovich for Newton's method
ArticleAbstract: We study the semilocal convergence of Newton's method in Banach spaces under a modification of the cPalabras claves:A priori error estimates, Hammerstein integral equation, Kantorovich's technique, Majorizing sequence, Newton's method, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusA semilocal convergence result for Newton's method under generalized conditions of Kantorovich
ArticleAbstract: From Kantorovich's theory we establish a general semilocal convergence result for Newton's method baPalabras claves:A priori error estimates, Conservative problem, Majorizing sequence, Newton's method, semilocal convergence, The Newton-Kantorovich theoremAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusA variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type
ArticleAbstract: We study nonlinear integral equations of mixed Hammerstein type using Newton's method as follows. WePalabras claves:Bratu's equation, Hammerstein's equation, Kantorovich's theorem, Majorizing sequence, Newton's method, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusExtending the applicability of Newton's method for a class of boundary value problems using the shooting method
ArticleAbstract: We use Newton's method to approximate locally unique solutions for a class of boundary value problemPalabras claves:boundary value problem, Lipschitz condition, Newton's method, Shooting methodAutores:Argyros I.K., Daniel González, Gutiérrez J.M., Johan CeballosFuentes:scopusExtending the applicability of Newton's method for k-Fréchet differentiable operators in Banach spaces
ArticleAbstract: We extend the applicability of Newton's method for k-Fréchet differentiable operators in a Banach spPalabras claves:A priori error estimates, Hammerstein integral equation, Majorizing sequence, Newton's method, semilocal convergence, The Newton-Kantorovich theoremAutores:Argyros I.K., Daniel GonzálezFuentes:scopusExtensions on a local convergence result by Dennis and Schnabel for Newton's method with applications
ArticleAbstract: The aim of this article is to extend the applicability of Newton's method involving k-Fréchet differPalabras claves:local of convergence, Newton's method, Order of convergenceAutores:Argyros I.K., Argyros M., Ceballos M., Daniel González, Johan CeballosFuentes:scopusNew improvement of the domain of parameters for newton's method
ArticleAbstract: There is a need to extend the convergence domain of iterative methods for computing a locally uniquePalabras claves:domain, IMPROVEMENT, Newton's methodAutores:Amorós C., Argyros I.K., Daniel González, Magreñán A.A., Regmi S., Sarría Í.Fuentes:scopusHow to apply Newton's method to operators with unbounded second derivative
Conference ObjectAbstract: The problem of finding the roots of a nonlinear equation has a long history. Although some nonlinearPalabras claves:Kantorovich's conditions, majorizing sequences, Newton's method, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusOn the local convergence of Newton's method under generalized conditions of Kantorovich
ArticleAbstract: Following an idea similar to that given by Dennis and Schnabel (1996) in [2], we prove a local convePalabras claves:local convergence, Newton's method, Order of convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusMajorizing sequences for Newton's method from initial value problems
ArticleAbstract: The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton'sPalabras claves:Bratu's equation, Kantorovich's technique, Majorizing sequence, Newton's method, Order of convergence, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopus