On the quadratic convergence of the Aitken $\Delta^2$ process
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1770-1774
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The Aitken $\Delta^2$ method for finding fixed points of scalar mappings is interpreted as a modification of the Wegstein method. Based on this approach, conditions for the quadratic convergence of this method are obtained for various situations of convergence/divergence of simple iteration. An algorithm for calculating fixed points that keeps track of these situations is presented.
@article{ZVMMF_2011_51_10_a1,
author = {V. M. Verzhbitskii and I. F. Yumanova},
title = {On the quadratic convergence of the {Aitken} $\Delta^2$ process},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1770--1774},
publisher = {mathdoc},
volume = {51},
number = {10},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a1/}
}
TY - JOUR AU - V. M. Verzhbitskii AU - I. F. Yumanova TI - On the quadratic convergence of the Aitken $\Delta^2$ process JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2011 SP - 1770 EP - 1774 VL - 51 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a1/ LA - ru ID - ZVMMF_2011_51_10_a1 ER -
%0 Journal Article %A V. M. Verzhbitskii %A I. F. Yumanova %T On the quadratic convergence of the Aitken $\Delta^2$ process %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2011 %P 1770-1774 %V 51 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a1/ %G ru %F ZVMMF_2011_51_10_a1
V. M. Verzhbitskii; I. F. Yumanova. On the quadratic convergence of the Aitken $\Delta^2$ process. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1770-1774. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a1/