Geodesic
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
Applications of Mathematics, Tome 28 (1983) no. 1, pp. 21-31
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1983.103999
Classification : 47H07, 47J25, 65J15
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 
@article{10_21136_AM_1983_103999,
     author = {Schneider, Norbert},
     title = {Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods},
     journal = {Applications of Mathematics},
     pages = {21--31},
     year = {1983},
     volume = {28},
     number = {1},
     doi = {10.21136/AM.1983.103999},
     mrnumber = {0684708},
     zbl = {0521.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.103999/}
}
TY  - JOUR
AU  - Schneider, Norbert
TI  - Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
JO  - Applications of Mathematics
PY  - 1983
SP  - 21
EP  - 31
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.103999/
DO  - 10.21136/AM.1983.103999
LA  - en
ID  - 10_21136_AM_1983_103999
ER  - 
%0 Journal Article
%A Schneider, Norbert
%T Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
%J Applications of Mathematics
%D 1983
%P 21-31
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.103999/
%R 10.21136/AM.1983.103999
%G en
%F 10_21136_AM_1983_103999
Schneider, Norbert. Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods. Applications of Mathematics, Tome 28 (1983) no. 1, pp. 21-31. doi: 10.21136/AM.1983.103999

[1] L. Kantorovich: The method of successive approximations for functional equations. Acta Math. 71 (1939), 63-97. | DOI | MR

[2] W. A. J. Luxemburg A. C. Zaanen: Riesz Spaces. North-Holland Publishing Company (1971). | MR

[3] J. M. Ortega W. C. Rheinboldt: Iterative solutions of nonlinear equations in several variables. Academic Press (1970). | MR

[4] A. Ostrowski: Solution of Equations and Systems of Equations. Academic Press (1966). | MR | Zbl

[5] J. W. Schmidt: Eingrenzung von Lösungen nichtlinearer Gleichungen durch Verfahren rnit höherer Konvergenzgeschwindigkeit. Computing 8, 208 - 215 (1971). | DOI | MR

[6] J. W. Schmidt H. Leonhardt: Eingrenzung von Lösungen mit Hilfe der Regula falsi. Computing 6 (1970), 318-329. | DOI | MR

[7] N. Schneider: Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes. Computing, to appear. | MR | Zbl

[8] J. Vandergraft: Newton's method for convex operators in partially ordered spaces. SIAM, J. Numer. Anal. 4 (1967), 406-432. | DOI | MR | Zbl

Cité par Sources :