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

Romero Alvarez, Natalia; Hernández Verón, Miguel Angel

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

Revista:

Grazer Mathematische Berichte

ISSN: 1016-7692

Any de publicació: 2007

Volum: 351

Pàgines: 37-51

Tipus: Article

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

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Resum

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