Ostrowski-Kantorovich theorem and -order of convergence of Halley method in Banach spaces
Commentationes Mathematicae Universitatis Carolinae (1993)
- Volume: 34, Issue: 1, page 153-163
- ISSN: 0010-2628
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Abstract
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topChen, Dong. "Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 153-163. <http://eudml.org/doc/247494>.
@article{Chen1993,
abstract = {Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of $S$-order of convergence and sufficient asymptotic error bound will be discussed.},
author = {Chen, Dong},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear operator equations; Banach spaces; Halley type method; Ostrowski-Kantorovich convergence theorem; Ostrowski-Kantorovich assumptions; optimal error bound; $S$-order of convergence; sufficient asymptotic error bound; Halley method; Banach spaces; Ostrowski-Kantorovich theorem; error bound; Newton-Kantorovich theorem; -order of convergence},
language = {eng},
number = {1},
pages = {153-163},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces},
url = {http://eudml.org/doc/247494},
volume = {34},
year = {1993},
}
TY - JOUR
AU - Chen, Dong
TI - Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 153
EP - 163
AB - Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of $S$-order of convergence and sufficient asymptotic error bound will be discussed.
LA - eng
KW - nonlinear operator equations; Banach spaces; Halley type method; Ostrowski-Kantorovich convergence theorem; Ostrowski-Kantorovich assumptions; optimal error bound; $S$-order of convergence; sufficient asymptotic error bound; Halley method; Banach spaces; Ostrowski-Kantorovich theorem; error bound; Newton-Kantorovich theorem; -order of convergence
UR - http://eudml.org/doc/247494
ER -
References
top- Dong Chen, On a New Definition of Order of Convergence in General Iterative Methods I: One Point Iterations, Research Report No. 7, Department of Mathematical Sciences, University of Arkansas, 1991.
- Dong Chen, On a New Definition of Order of Convergence in General Iterative Methods II: Multipoint Iterations, Research Report No. 8, Department of Mathematical Sciences, University of Arkansas, 1991.
- Kantorovich L.V., Akilov G.P., Functional Analysis in Normed Spaces, Pergaman Press, New York, 1964. Zbl0127.06104MR0213845
- Ostrowski A.M., Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York, 3rd ed., 1973. Zbl0304.65002MR0359306
- Taylor A.E., Introduction to Functional Analysis, Wiley, New York, 1957. Zbl0654.46002MR0098966
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