CONVERGENCE CRITERION OF INEXACT METHODS FOR OPERATORS WITH H¨OLDER CONTINUOUS DERIVATIVES

Convergence criterion of the inexact methods is established for operators with h¨older continuous first derivatives. An application to a special nonlinear Hammerstein integral equation of the second kind is provided.

[1]  Benedetta Morini,et al.  Inexact Methods in the Numerical Solution of Stiff Initial Value Problems , 1999, Computing.

[2]  Chong Li,et al.  Local convergence of inexact methods under the Hölder condition , 2008 .

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

[4]  Raymond H. Chan,et al.  On the Convergence Rate of a Quasi-Newton Method for Inverse Eigenvalue Problems , 1999 .

[5]  Xinghua Wang,et al.  Convergence of Newton's method and inverse function theorem in Banach space , 1999, Math. Comput..

[6]  Xinghua Wang,et al.  Convergence of Newton's method and uniqueness of the solution of equations in Banach space , 2000 .

[7]  José Antonio Ezquerro,et al.  Generalized differentiability conditions for Newton's method , 2002 .

[8]  I. Stakgold Green's Functions and Boundary Value Problems , 1979 .

[9]  Wang Xinghua,et al.  Convergence of Newton's method and inverse function theorem in Banach space , 1999 .

[10]  A. H. Sherman On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations , 1978 .

[11]  M. A. Hernández The Newton Method for Operators with Hölder Continuous First Derivative , 2001 .

[12]  Raymond H. Chan,et al.  The Inexact Newton-Like Method for Inverse Eigenvalue Problem , 2003 .

[13]  José Antonio Ezquerro,et al.  On an Application of Newton's Method to Nonlinear Operators with w-Conditioned Second Derivative , 2002, BIT Numerical Mathematics.

[14]  T. J. Ypma Local convergence of difference Newton-like methods , 1983 .

[15]  B. Morini,et al.  Inexact Methods: Forcing Terms and Conditioning , 2000 .

[16]  C. G. Broyden A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

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

[18]  P. Brown,et al.  Matrix-free methods for stiff systems of ODE's , 1986 .