Interpolation in linear normed spaces and applications

Abstract

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

Keywords

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.

References

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Cite this paper as:

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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