Journal of applied mathematics & informatics

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

CONCERNING THE MONOTONE CONVERGENCE OF THE METHOD OF TANGENT HYPERBOLAS

  • Published : 2000.05.01

⟨ Previous Next ⟩

Abstract

We provide sufficient conditions for the monotone convergence of a Chebysheff-Halley-type method or method of tangent hyperbolas in a partially ordered topological space setting. The famous kantorovich theorem on fixed points is used here.

Keywords

References

  1. Bull. Austral. Math. Soc. v.45 On the monotone convergence of general Newton-like methods I.K. Argyros;F. Szidarovszky
  2. Appl. Math. Letters v.6 no.5 On the convergence of a Chebysheff-Halley type method under Newton-Kantorovich hypotheses I.K. Argyros
  3. Pure Mathematics and Applications v.4 no.3 On the convergence of an Euler-Chebysheff-type method under Newton-Kantorovich hypotheses I.K. Argyros
  4. Appl. Math. and Comp. v.58 A note on the Halley method in Banach spaces I.K. Argyros
  5. The Theory and Applications of Iteration Methods I.K. Argyros;F. Szidarovszky
  6. Acta Math. v.71 The method of successive approximation for functional equations L.V. Kantorovich
  7. Dokl. Akad. Nauk. SSSR v.88 An analog of the process of tangent hyperbolas for general functional equations (Russian) M.A. Mertvecova
  8. Uwephi Mat. Nauk. v.9 On Chebysheff's method for functional equations (Russian) M.T. Necepurenko
  9. Numer. Funct. Anal. and Optimiz. v.7 no.1 On an iterative algorithm of order 1.839... for solving nonlinear operator equations F.A. Potra
  10. Dokl. Akad. Nauk. SSSR v.158 Iteration methods with divided differences of the second order (Russian) S. Ul'm
  11. Sovitet Math. Dokl. v.5
  12. SIAM J. Numer. Anal. v.4 Newton's method for convex operators in partially ordered spaces J.A. Vandergraft