Geodesic
A note on the convergence of nonstationary finite-difference analogues
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 204-211 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An efficient modification of a finite-difference analogue of Halley's method is proposed. An iterative procedure ensures that the approximations converge to the desired root of the nonlinear equation $f(x)=0$. 
@article{ZVMMF_2005_45_2_a2,
     author = {V. Hristov and A. I. Iliev and N. V. Kyurkchiev},
     title = {A note on the convergence of nonstationary finite-difference analogues},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {204--211},
     year = {2005},
     volume = {45},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a2/}
}
TY  - JOUR
AU  - V. Hristov
AU  - A. I. Iliev
AU  - N. V. Kyurkchiev
TI  - A note on the convergence of nonstationary finite-difference analogues
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 204
EP  - 211
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a2/
LA  - en
ID  - ZVMMF_2005_45_2_a2
ER  - 
%0 Journal Article
%A V. Hristov
%A A. I. Iliev
%A N. V. Kyurkchiev
%T A note on the convergence of nonstationary finite-difference analogues
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 204-211
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a2/
%G en
%F ZVMMF_2005_45_2_a2
V. Hristov; A. I. Iliev; N. V. Kyurkchiev. A note on the convergence of nonstationary finite-difference analogues. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 2, pp. 204-211. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_2_a2/

[1] Liangzang X., Xiangjiand M., “Convergence of an iteration method without derivative”, Numer. Math. J. Chinese Univ. English Ser., 11 (2002), 113–120 | MR | Zbl

[2] Ralston A., A first course in numerical analysis, McGraw-Hill, New York, 1965 | MR | Zbl

[3] Xinghua W., Shiming Z., Danfu H., “Convergence on Euler's series, the iteration of Euler's and Halley's families”, Acta Math. Sinica, 33 (1990), 721–738 | MR | Zbl

[4] Traub J., Iterative method for solution of equations, Chelsea Publ. Co., New York, 1982 | Zbl

[5] Xinghua W., “On the zero of analytic functions”, Nature J., 4:6 (1981), 474 (in Chinese)