Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

A MESH-INDEPENDENCE PRINCIPLE FOR OPERATORS EQUATIONS AND THE STEFFENSEN METHOD

  • Published : 1997.06.01

⟨ Previous Next ⟩

Abstract

In this study we prove the mesh-independence principle via Steffensen's method. This principle asserts that when Steffensen's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation then the behavior of th discretized process is asymptoti-cally the same as that for the original iteration. Local and semilo-cal convergencve results as well as an error analysis for Steffensen's method are also provided.

Keywords

References

  1. SIMA J. Numer. Anal. v.23 no.1 A mesh independence principle for operator equations and their discretizations Allgower, E.L.;Bohmer, K.;Potra, F.A.;Rheinboldt, W.C.
  2. Computing v.45 A mesh independence principle for operator equations and their discretizations under mild differentiability conditions Argyros, I.K.
  3. Acta Math. Hungarica v.60 no.1-2 On a mesh independence principle for operator equations and the secant method Argyros, I.K.
  4. Intern. J. Computer Math. v.52 on the discretization of Newton-like methods Argyros, I.K.
  5. The Theory and Application of Iteration Methods Argyros, I.K.;Szidarovsky, F.
  6. Revue d'analyse Numerique et de theorie de l'approximation v.23 no.1 On some iterative methods for solving nonlinear equations Catinas, E.
  7. Revue d'analyse Numerique et de theorie de l'approximation v.21 no.1 Sur une generalisation de la methods de Steffensen Pavaloiu, I.