An improved convergence analysis of Newton's method for twice Fréchet differentiable operators

• Autorzy: Ioannis K. Argyros , Sanjay K. Khattri
• Języki publikacji: EN

Abstrakty

EN

We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.

Kategorie tematyczne

• 49M15: Newton-type methods
• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 65N35: Spectral, collocation and related methods
• 65G99: None of the above, but in this section
• 65J20: Improperly posed problems; regularization
• 65H10: Systems of equations
• 65J15: Equations with nonlinear operators (do not use )
• 65B05: Extrapolation to the limit, deferred corrections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2013
• Tom: 40
• Numer: 4
• Strony: 459-481

Daty

wydano

2013

Twórcy

autor

Ioannis K. Argyros

• Department of Mathematical Sciences, Cameron University, Lawton, OK 73505-6377, U.S.A.

autor

Sanjay K. Khattri

• Department of Engineering, Stord/Haugesund University College, N-414 Stord, Norway

Identyfikatory

DOI

10.4064/am40-4-6