A two-step Steffensen's method under modified convergence conditions

By Sergio Amat, Sonia Busquier. 2006

48 citations recorded by the source corpus.

A simplification of a third order iterative method is proposed. The main advantage of this method is that it does not need to evaluate neither any Frechet derivative nor any bilinear operator. A semilocal convergence theorem in Banach spaces, under modified Kantorovich conditions, is analyzed. A local convergence analysis is also performed. Finally, some numerical results are presented.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/532601851f8596db3f57e8aedfea6490d4f9ca40

How researchers see this paper

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In Modeling and Simulation

1. Sergio Plaza
2. Sonia Busquier
3. Sergio Amat

In Numerical Analysis

1. Sergio Plaza
2. Sonia Busquier
3. Sergio Amat
4. Herbert H. H. Homeier

Citations in the corpus

• Chaotic dynamics of a third-order Newton-type method (2010, methodology): “We are interested to analyze the dynamics of the following third-order iterative root-finding method [13,15,1,3] ⎪⎪⎨ ⎪⎪⎩ yn = xn − f (xn) f ′(xn) , xn+1 = yn − f (yn) f ′(xn) .”