论文信息 - A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative

A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative

Abstract In this paper, we give a new semi-local convergence theorem for inexact Newton method under the assumption that the Frechet derivative f ′ is H o ¨ lder continuous. An affine invariant theorem for inexact Newton method and some corollaries are given as well.

[1] J. M. Martínez,et al. Inexact Newton methods for solving nonsmooth equations , 1995 .

[2] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[3] Kenneth R. Jackson,et al. The numerical solution of large systems of stiff IVPs for ODEs , 1996 .

[4] M. Fukushima,et al. "Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" , 2010 .

[5] Qingbiao Wu,et al. Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative , 2006 .

[6] R. Dembo,et al. INEXACT NEWTON METHODS , 1982 .

[7] Homer F. Walker,et al. Globally Convergent Inexact Newton Methods , 1994, SIAM J. Optim..

[8] Igor Moret,et al. A kantorovich-type theorem for inexact newton methods , 1989 .

[9] P. Deuflhard,et al. Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods , 1979 .

[10] T. Ypma,et al. Affine invariant convergence results for Newton's method , 1982 .

[11] Benedetta Morini,et al. Convergence behaviour of inexact Newton methods , 1999, Math. Comput..

[12] Jinhai Chen,et al. Convergence behaviour of inexact Newton methods under weak Lipschitz condition , 2006 .

[13] T. Ypma. Local Convergence of Inexact Newton Methods , 1984 .

[14] Ioannis K. Argyros. A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative , 1999 .