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Title: Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods (English)
Author: Schneider, Norbert
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 28
Issue: 1
Year: 1983
Pages: 21-31
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved. (English)
Keyword: derivative free methods
Keyword: upper and lower bounds
Keyword: partially ordered Banach spaces
Keyword: monotone enclosure of solutions
Keyword: Regula-falsi-like methods
Keyword: generalized divided difference operators
Keyword: existence
Keyword: convergence
Keyword: numerical example
Keyword: iterative method
MSC: 47H07
MSC: 47J25
MSC: 65J15
idZBL: Zbl 0521.65042
idMR: MR0684708
DOI: 10.21136/AM.1983.103999
Date available: 2008-05-20T18:20:52Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] L. Kantorovich: The method of successive approximations for functional equations.Acta Math. 71 (1939), 63-97. MR 0000095, 10.1007/BF02547750
Reference: [2] W. A. J. Luxemburg A. C. Zaanen: Riesz Spaces.North-Holland Publishing Company (1971). MR 0511676
Reference: [3] J. M. Ortega W. C. Rheinboldt: Iterative solutions of nonlinear equations in several variables.Academic Press (1970). MR 0273810
Reference: [4] A. Ostrowski: Solution of Equations and Systems of Equations.Academic Press (1966). Zbl 0222.65070, MR 0216746
Reference: [5] J. W. Schmidt: Eingrenzung von Lösungen nichtlinearer Gleichungen durch Verfahren rnit höherer Konvergenzgeschwindigkeit.Computing 8, 208 - 215 (1971). MR 0314265, 10.1007/BF02234103
Reference: [6] J. W. Schmidt H. Leonhardt: Eingrenzung von Lösungen mit Hilfe der Regula falsi.Computing 6 (1970), 318-329. MR 0286275, 10.1007/BF02238816
Reference: [7] N. Schneider: Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes.Computing, to appear. Zbl 0438.65050, MR 0620236
Reference: [8] J. Vandergraft: Newton's method for convex operators in partially ordered spaces.SIAM, J. Numer. Anal. 4 (1967), 406-432. Zbl 0161.35302, MR 0221794, 10.1137/0704037


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