The Catalan numbers in the approximation of roots of quadratic polynomials.

  1. Romero Alvarez, Natalia
  2. Hernández Verón, Miguel Angel
Revue:
Grazer Mathematische Berichte

ISSN: 1016-7692

Année de publication: 2007

Volumen: 351

Pages: 37-51

Type: Article

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Projets liés

Diferentes tipos de condiciones iniciales para la convergencia semilocal en la aproximación de ceros de operadores no lineales. Aplicaciones.

2005/00064/001

Résumé

The authors construct a family of Newton-like methods with prefixed order of convergence and furnish semi-local convergence results for the family and a global convergence result for some iterative processes. The authors also present fractal pictures that arise from the iterative methods of the family when they are applied to approximate a root of the quadratic polynomial f(t)=t2−5t+4. This shows that iterative methods with prefixed order are not globally convergent, but general convergence for them can be obtained