Interpolation in linear normed spaces and applications

Let \(X,Y\) be two normed spaces and \(P:X\rightarrow Y\) a nonlinear operator. We construct the Lagrange interpolation operator for \(P\), in the Newton form, with the aid of divided differences constructed by multilinear operators, which also provide estimations of the remainder. Applying the Lagrange inverse interpolation polynomial leads us to a general iteration method. As particular instances, we obtain the chord method and a Chebyshev type method.

Ion Păvăloiu

Lagrange interpolation in normed spaces; generalized divided differences; multilinear operators, inverse interpolation; chord method; Chebyshev method; chord method in normed spaces; Chebyshev method in normed spaces.

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I. Păvăloiu, Intérpolation dans des éspaces linéaires normées et applications, Mathematica, 12(35) (1970) no. 1, pp. 149-158 (in French).

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