Sur une généralisation de la méthode de Steffensen

On a generalization of the Steffensen method

Authors

  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Abstract views: 205

Abstract

We extend the Steffensen method for solving the equation \(f\left( x\right)=0\) to the setting of the Banach spaces, \(f:X\rightarrow X,\ X\) a Banach space. Considering another equation \(x-g\left( x\right) =0\), equivalent to the above one and assuming certain conditions on the first and second order divided differences of \(f\) we obtain a semilocal convergence result for the method \[x_{n+1}=x_{n}-\left[ x_{n},g\left( x_{n}\right) ;f\right]^{-1}f\left( x_{n}\right) ,~x_{0}\in X.\]

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References

Balasz M. şi Goldner G., Diferenţe divizate în spaţii Banach şi unele aplicaţii ale lor. St. cerc. mat. 21, 7, (1969), pp.985-995.

Diaconu Adrian, Interpolation dans les espaces arbitraits. Méthodes itératives pour le résolution des équations opérationnelles obtenus par ;l'interpolations inverse. III Research Seminar of Functional Analysis and Numerical Methodes, Preprint Nr.1 1985, pp.21-70.

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Păvăloiu I. Sur la méthode de Steffensen pour la résolution des équations opérationnelles non linéaires. Revue Roumaine de Mathematiques pures et appliquées. XIII, 1, (1968), pp.149/158.

Păvăloiu I. Introducere în teoria aproximării soluţiilor ecuaţiilor. Ed. Dacia, Cluj-Napoca, 1976.

Ul'm, S., Ob obobscennîh razdelennîh raznostiah I, Izv. Acad. Nauk. Estenoskoi S.S.R. 16, 1, (1967), pp.13-26.

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Published

1992-02-01

How to Cite

Păvăloiu, I. (1992). Sur une généralisation de la méthode de Steffensen: On a generalization of the Steffensen method. Rev. Anal. Numér. Théor. Approx., 21(1), 59–65. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1992-vol21-no1-art8

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