Sur l'approximation des solutions des équations à l'aide des suites à éléments dans un espaces de Banach

On the approximation of solutions of equations using sequences with elements in a Banach space

Authors

  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Abstract views: 269

Abstract

Let \(X\) be a Banach space, \(Y\) a normed space \(P:X\rightarrow Y\) a nonlinear operator and the equation \(P\left( x\right) =0\) with solution \(x^{\ast}\). Consider \(\Sigma:=\left( x_{n}\right) _{n\geq0}\) a sequence from \(X\) and define the convergence order of \(\Sigma\) with respect to the solution of equation \(P\left( x\right) =0\). We give a general result with sufficient conditions such that the sequence \(\Sigma\) converge to the solution \(x^{\ast}\) with a given convergence order.

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References

Ghinea, Monique, Sur la résolution des équations opérationnelles dans les espaces de Banach. (French) Rev. Française Traitement Information Chiffres 8 1965 3-22, MR0183111.

Păvăloiu, I., Sur les procédés itératifs à un ordre élevé de convergence. (French) Mathematica (Cluj) 12(35) (1970), 309-324, MR0339486.

Traub, J. F., Iterative methods for the solution of equations. Prentice-Hall Series in Automatic Computation Prentice-Hall, Inc., Englewood Cliffs, N.J. 1964 xviii+310 pp., MR0169356.

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Published

1976-02-01

How to Cite

Păvăloiu, I. (1976). Sur l’approximation des solutions des équations à l’aide des suites à éléments dans un espaces de Banach: On the approximation of solutions of equations using sequences with elements in a Banach space. Anal. Numér. Théor. Approx., 5(1), 63–67. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1976-vol5-no1-art6

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