Geodesic
About the computation of simple and multiple roots of nonlinear equation
Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 57-64.

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

Classical and generalized Newton methods as applied to the calculation of simple and multiple roots of nonlinear equation were examined. Algorithms for determining root's order during calculation were developed for both mentioned methods, which also allow to accelerate convergence for multiple roots. These algorithms are able to calculate roots even of a big order with a high accuracy. Careful examination of the algorithm details was accomplished, which allowed to write more precise and reliable program than existing standard ones. 
@article{MM_2008_20_7_a5,
     author = {N. N. Kalitkin and I. P. Poshivaylo},
     title = {About the computation of simple and multiple roots of nonlinear equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {57--64},
     publisher = {mathdoc},
     volume = {20},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/}
}
TY  - JOUR
AU  - N. N. Kalitkin
AU  - I. P. Poshivaylo
TI  - About the computation of simple and multiple roots of nonlinear equation
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 57
EP  - 64
VL  - 20
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/
LA  - ru
ID  - MM_2008_20_7_a5
ER  - 
%0 Journal Article
%A N. N. Kalitkin
%A I. P. Poshivaylo
%T About the computation of simple and multiple roots of nonlinear equation
%J Matematičeskoe modelirovanie
%D 2008
%P 57-64
%V 20
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/
%G ru
%F MM_2008_20_7_a5
N. N. Kalitkin; I. P. Poshivaylo. About the computation of simple and multiple roots of nonlinear equation. Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 57-64. http://geodesic.mathdoc.fr/item/MM_2008_20_7_a5/

[1] Opredelenie kratnosti kornya metodom Nyutona, http://www.exponenta.ru/educat/class/class.asp

[2] Gavurin M. K., “Nelineinye funktsionalnye uravneniya i nepreryvnye analogi iterativnykh metodov”, Izv. Vuzov. Matematika, 1958, no. 5(6), 18–31 | MR | Zbl

[3] Zhidkov E. P., Puzynin I. V., “Ob odnom metode vvedeniya parametra pri reshenii kraevykh zadach dlya nelineinykh obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, ZhVM i MF, 7:5 (1967), 1086–1095 | Zbl

[4] Ermakov V. V., Kalitkin N. N., “Optimalnyi shag i regulyarizatsiya metoda Nyutona”, ZhVM i MF, 21:2 (1981), 491–497 | MR | Zbl