| 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:
|
http://hdl.handle.net/10338.dmlcz/103999 |
| . |
| 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 |
| . |
