Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods

Norbert Schneider

Aplikace matematiky (1983)

  • Volume: 28, Issue: 1, page 21-31
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Schneider, Norbert. "Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods." Aplikace matematiky 28.1 (1983): 21-31. <http://eudml.org/doc/15271>.

@article{Schneider1983,
abstract = {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.},
author = {Schneider, Norbert},
journal = {Aplikace matematiky},
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; 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},
language = {eng},
number = {1},
pages = {21-31},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods},
url = {http://eudml.org/doc/15271},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Schneider, Norbert
TI - Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 1
SP - 21
EP - 31
AB - 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.
LA - eng
KW - 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; 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
UR - http://eudml.org/doc/15271
ER -

References

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  1. L. Kantorovich, 10.1007/BF02547750, Acta Math. 71 (1939), 63-97. (1939) MR0000095DOI10.1007/BF02547750
  2. W. A. J. Luxemburg A. C. Zaanen, Riesz Spaces, North-Holland Publishing Company (1971). (1971) Zbl0231.46014MR0511676
  3. J. M. Ortega W. C. Rheinboldt, Iterative solutions of nonlinear equations in several variables, Academic Press (1970). (1970) Zbl0241.65046MR0273810
  4. A. Ostrowski, Solution of Equations and Systems of Equations, Academic Press (1966). (1966) Zbl0222.65070MR0216746
  5. J. W. Schmidt, 10.1007/BF02234103, Computing 8, 208 - 215 (1971). (1971) MR0314265DOI10.1007/BF02234103
  6. J. W. Schmidt H. Leonhardt, 10.1007/BF02238816, Computing 6 (1970), 318-329. (1970) Zbl0231.65053MR0286275DOI10.1007/BF02238816
  7. N. Schneider, Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes, Computing, to appear. Zbl0438.65050MR0620236
  8. J. Vandergraft, 10.1137/0704037, SIAM, J. Numer. Anal. 4 (1967), 406-432. (1967) Zbl0161.35302MR0221794DOI10.1137/0704037

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