Solving equations by interpolation


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.


Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)


Original title (in French)

La résolution des equations par intérpolation

English translation of the title

Solving equations by interpolation


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


Cite this paper as:

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

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