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.

Authors

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

[1] Balazs M. ¸si Bırsan F., Asupra unor metode iterative cu diferente divizate de ordinul doi si rapiditatea de convergenta de ordinul trei pentru rezolvarea ecuatiilor operationale nelineare. Studii si cercetari matematice 21, 7, 975-984 (1969).

[2] Balasz M. si Goldner G., Diferente divizate ın spatii Banach si unele aplicatii ale lor. Studii si cercetari matematice, 21, 7, 985-995 (1969).

[3] Janko B., Sur l’analogue de la m´ethode de Tch´ebycheff et de la methode des hyperboles tangentes. Mathematica, 2 (25), 2, 269-275 (1960).

[4] Moldovan E., Interpolarea in spatii abstracte. Studii si cercetari de matematica. (Cluj), X, 2 239-335 (1959).

[5] Ostrowski A. M., Resenie uravnenii i sistem uravnenii M. Izd-vo in lit (1963).

[6] Popoviciu T., Sur la delimitation de lerreur dans l’approximation des racines d’une ´equation par interpolation lineaire ou quadratique. Revue Roumaine de mathematiques pures et appliquees 13, 1, 75–78 (1968).
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[7] Schmidt J. W., Konvergenzgeschwindigkeit der Regula falsi und des SteffensenVerfahrens im Banachraum Z.A.M.M. 46, 2 146–148 (1966).

[8] Schmidt J. W. and Schwetlick H., Ableitungsfreie Verfahren mit hohever Konvergenzgeschwindigkeit. Computing 3, 215–226 (1968).

[9] Sergeev A.S., O metode hord. Sibirski mat. jurnal 1, 2, 282–289 (1961).

[10] S. Ul’m, Obobobscennıh razdelennıh raznostiah I Izv. Akad. Nauk. Estonskoi S.S.R. 16, 1, 13–26 (1967).

[11] Ul’m S., Ob obobscennıh razdelennıh raznostiah II Izv. Akad. Nauk Estonskoi S.S.R., 16, 2, 146–155 (1967).

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About this paper

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).

Journal

Mathematica

Publisher Name

Academia Republicii S.R.

DOI

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