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Schneider, Norbert
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods. (English). Aplikace matematiky, vol. 28 (1983), issue 1, pp. 21-31
MSC: 47H07, 47J25, 65J15 | MR 0684708 | Zbl 0521.65042 | DOI: 10.21136/AM.1983.103999
Keywords:
derivative free methods; upper and lower bounds; partially ordered Banach spaces; monotone enclosure of solutions; Regula-falsi-like methods; generalized divided difference operators; existence; convergence; numerical example; iterative method
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.
References:
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[2] W. A. J. Luxemburg A. C. Zaanen: Riesz Spaces. North-Holland Publishing Company (1971). MR 0511676
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[4] A. Ostrowski: Solution of Equations and Systems of Equations. Academic Press (1966). MR 0216746 | Zbl 0222.65070
[5] J. W. Schmidt: Eingrenzung von Lösungen nichtlinearer Gleichungen durch Verfahren rnit höherer Konvergenzgeschwindigkeit. Computing 8, 208 - 215 (1971). DOI 10.1007/BF02234103 | MR 0314265
[6] J. W. Schmidt H. Leonhardt: Eingrenzung von Lösungen mit Hilfe der Regula falsi. Computing 6 (1970), 318-329. DOI 10.1007/BF02238816 | MR 0286275
[7] N. Schneider: Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes. Computing, to appear. MR 0620236 | Zbl 0438.65050
[8] J. Vandergraft: Newton's method for convex operators in partially ordered spaces. SIAM, J. Numer. Anal. 4 (1967), 406-432. DOI 10.1137/0704037 | MR 0221794 | Zbl 0161.35302
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