Geodesic
Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1093-1102

Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions under which two- and three-point iterative methods have the order of convergence $p$ ($2\leqslant p\leqslant 8$) are formulated for the first time. These conditions can be effectively used to prove the convergence of iterative methods. In particular, the order of convergence of some known optimal methods is verified using the proposed sufficient convergence tests. The optimal set of parameters making it possible to increase the order of convergence is found. It is shown that the parameters of the known iterative methods with the optimal order of convergence have the same asymptotic behavior. The simplicity of choosing the parameters of the proposed methods is an advantage over the other known methods. 
@article{ZVMMF_2017_57_7_a1,
     author = {T. Zhanlav and V. Ulziibayar and O. Chuluunbaatar},
     title = {Necessary and sufficient conditions for the convergence of two- and three-point {Newton-type} iterations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1093--1102},
     publisher = {mathdoc},
     volume = {57},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a1/}
}
TY  - JOUR
AU  - T. Zhanlav
AU  - V. Ulziibayar
AU  - O. Chuluunbaatar
TI  - Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1093
EP  - 1102
VL  - 57
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a1/
LA  - ru
ID  - ZVMMF_2017_57_7_a1
ER  - 
%0 Journal Article
%A T. Zhanlav
%A V. Ulziibayar
%A O. Chuluunbaatar
%T Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1093-1102
%V 57
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a1/
%G ru
%F ZVMMF_2017_57_7_a1
T. Zhanlav; V. Ulziibayar; O. Chuluunbaatar. Necessary and sufficient conditions for the convergence of two- and three-point Newton-type iterations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1093-1102. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a1/