A-posteriori bounds for Steffensen-like methods

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  • Rudolf L. Voller Universitat Dusseldorf, Germany
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References

Balázs, M., A note on the convergence of Steffensen's method. Anal. Numér. Théor. Approx. 10 (1981), no. 1, 5-10, MR0670629.

Balázs, M.; Goldner, G., On Steffensen's method in Fréchet spaces. (Romanian summary) Studia Univ. Babeş-Bolyai Math. 28 (1983), 34-37, MR0743571.

Baptist, P., Konvergenz und monotone Einschliessung für das Steffensen-Verfahren. (German) [Convergence and monotone inclusion for the Steffensen procedure] Elem. Math. 37 (1982), no. 2, 33-40, MR0651249, https://www.e-periodica.ch/cntmng?pid=edm-001:1982:37::202

Bel'tyukov, B.A.: A method of solving nonlinear functional equation, URSS Comp. Math. Phys., 5, 210-217, 1965.

Chen, Kuo-Wang, Generalization of Steffensen's method for operator equations. Comment. Math. Univ. Carolinae 5 1964 47-77, MR0169399.

Döring, B., Über das Newtonsch Näherungsverfahren, Math.-Phys. Sem. - Ber., 16, 27-40, 1969.

Hofmann, Wolf, Monotonieeigenschaften des Steffensen-Verfahrens. (German) Aequationes Math. 12 (1975), 21-31, MR0368417, https://doi.org/10.1007/BF01834035

Johnson, L. W., Scholz, D. R., On Steffensen's method. SIAM J. Numer. Anal. 5 1968 296-302, MR0228150, https://doi.org/10.1137/0705026

Kantorovich, L. V., Akilov, G. P., Functional analysis. Translated from the Russian by Howard L. Silcock. Second edition. Pergamon Press, Oxford-Elmsford, N.Y., 1982. xiv+589 pp. ISBN: 0-08-023036-9; 0-08-026486-7 46-01 (47-01 65-01), MR0664597.

Koppel', H., Convergence of the generalized method of Steffensen. (Russian. Estonian, English summary) Eesti NSV Tead. Akad. Toimetised Füüs.-Mat. Tehn.-tead. Seer. 15 1966 531--539., MR0207197.

Mönch, Wolfgang, Inversionsfreie Verfahren zur Einschliessung von Nullstellen nichtlinearer Operatoren. (German) Beiträge Numer. Math. 2 (1974), 125-136, MR0426419.

Ortega, J. M.; Rheinboldt, W. C., Iterative solution of nonlinear equations in several variables. Academic Press, New York-London 1970 xx+572 pp., MR0273810.

Schmidt, Jochen W., Konvergenzgeschwindigkeit der Regula falsi und des Steffensen-Verfahrens im Banachraum. (German) Z. Angew. Math. Mech. 46 1966 146--148, MR0210317.

Schmidt, J. W., Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip. (German) Period. Math. Hungar. 5 (1974), 187-193, MR0356487.

Schneider, Norbert, Results about monotone convergence of Steffensen-like-methods. BIT 21 (1981), no. 3, 347-354, MR0640935.

Steffensen, J.F., Remarks on iteration, Skand. Aktuar. Tidskv., 16, 64-72, 1933.

Ul'm, S.Y., Extension of Steffensen's method for solving nonlinear operator equations, USSR Comp. Math., 4, 159-165, 1964.

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Published

1985-08-01

How to Cite

Voller, R. L. (1985). A-posteriori bounds for Steffensen-like methods. Anal. Numér. Théor. Approx., 14(2), 159–170. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1985-vol14-no2-art10

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Vol. 14 No. 2 (1985)

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