El método de Newton en espacios de Banach

Newton's method is a well known iterative method to solve a nonlinear equation F(x) = 0. We analyze the convergence of this method for operators defined between two Banach spaces, so our results can be applied in a wide range of problems, such as real or complex equations, nonlinear systems of equations, differential or integral equations. Firstly we study Newton's method in terms of the linear operator LFx=F' x-1F ''x F 'x1 Fx. In this sense, new convergence results are given in terms of this operator. Another part of this report is devoted to the study of Newton's method assuming that F satisfies different conditions from the classical ones (Kantorovich). Finally, as an acceleration of Newton's method, a new third order iterative process is obtained. Its basic properties (convergence, unicity of solution, error estimates, etc.) are analysed. This work is mainly theoretical although some results are illustrated with examples.

Grantor dc:publisher

Universidad de La Rioja (España)

Year dc:date

1995

Author dc:creator

• Gutiérrez Jiménez, José Manuel

Contributors dc:contributor

• Hernández Verón, Miguel Angel (Universidad de La Rioja)

• Ecuaciones no lineares
• métodos iterativos
• método de Newton
• secuencias mayorizantes
• Nonlinear equations
• iterative methods
• Newton's method
• majorizing sequences

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Language dc:language

spa

Repository record dc:identifier

https://dialnet.unirioja.es/servlet/oaites?codigo=10

OAI identifier oai:identifier

oai:dialnet.unirioja.es:TES0000000216