Local convergence of Newton's method under a majorant condition in Riemannian manifolds

2012 ◽  
Vol 32 (4) ◽  
pp. 1696-1713 ◽  
Author(s):  
O. P. Ferreira ◽  
R. C. M. Silva
Keyword(s):  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Local Convergence ◽  
Newton's Method ◽  
Majorant Condition

scholarly journals On the Superlinear Convergence of Newton’s Method on Riemannian Manifolds

2017 ◽  
Vol 173 (3) ◽  
pp. 828-843 ◽  
Author(s):  
Teles A. Fernandes ◽  
Orizon P. Ferreira ◽  
Jinyun Yuan
Keyword(s):  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Superlinear Convergence ◽  
Newton's Method

scholarly journals Local convergence of Newton’s method on the Heisenberg group

2016 ◽  
Vol 300 ◽  
pp. 217-232
Author(s):  
Béchir Dali ◽  
Chong Li ◽  
Jinhua Wang
Keyword(s):  
Heisenberg Group ◽  
Newton’S Method ◽  
Local Convergence ◽  
Newton's Method

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

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