Solving equations by interpolation

Abstract

Let \(X,Y\) be normed spaces, \(G:X\rightarrow Y\) a nonlinear operator, and the nonlinar equation \(G\left( x\right) =0\). We define the divided differences of \(G\) and we give some examples of nonlinear operators on Banach spaces for which we construct the divided differences of different orders. We construct the Lagrange interpolation polynomial in the Newton form for \(G\). The solution of equation is a approximated by using the inverse interpolation Lagrange polynomial.

Authors

Ion Păvăloiu

Title

Original title (in French)

La résolution des equations par intérpolation

English translation of the title

Solving equations by interpolation

Keywords

divided difference in normed spaces, Lagrange inverse interpolation; multistep iterative method of Newton type

References

[1] A.M. Ostrowski, Resenie uravnenii i sistem uravnenii, Izd. inostr. lit. Moskva (1963).

[2] I. Pavaloiu, Interpolation dans les espaces lineaires normes et applications, Mathematica, Cluj, nr.12 (35), 2, (1970), pp. 309–324.

[3] I. Pavaloiu, Introducere in teoria aproximarii solutiilor ecuatiilor, Editura Dacia, 1976.

[4] T. Popoviciu, Introduction a la theorie des differences divisees, Bulletin mathematique de la societe Roumaine de Sciences, 42, 1, (1940) pp. 65–78.

[5] A.S. Sergeev, O metode hord, Sibirski mat. Jurnal, XI, (2), (1961), pp. 282–289.

[6] J.F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall, Series in Automatic Computation, 1964.

[7] S. Ul’m, Ob obobscennyh razdelennîh raznostiah, II, Izv. Nauk Estonskoi SSR, 16, 2, (1967), 146–155.

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Cite this paper as:

I. Păvăloiu, La résolution des equations par intérpolation, Mathématica, 23(46) (1981) no. 1, pp. 61-72 (in French).

Journal

Mathematica

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