Geodesic
The method of seconds with extrapolation for accurate calculation of manifold roots
Matematičeskoe modelirovanie, Tome 23 (2011) no. 6, pp. 33-58.

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

The problem is investigated to calculate accurately many fold roots of a nonlinear algebraic equation. The algorithm is constructed for founding of multiplicity of roots in frame of the method of seconds. The recurrent extrapolation is proposed to improve an accuracy in 100–1000 times. The FORTRAN code SECWEX is written. It gives the value of a root an asymptotically exact which is an estimation of it’s error and an estimation of it’s multiplicity. The code is robust when multiplicity is up to 10.
Mots-clés : equation solution
Keywords: multiple roots, Aitken extrapolation. 
@article{MM_2011_23_6_a2,
     author = {N. N. Kalitkin and L. V. Kuzmina},
     title = {The method of seconds with extrapolation for accurate calculation of manifold roots},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--58},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_6_a2/}
}
TY  - JOUR
AU  - N. N. Kalitkin
AU  - L. V. Kuzmina
TI  - The method of seconds with extrapolation for accurate calculation of manifold roots
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 33
EP  - 58
VL  - 23
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_6_a2/
LA  - ru
ID  - MM_2011_23_6_a2
ER  - 
%0 Journal Article
%A N. N. Kalitkin
%A L. V. Kuzmina
%T The method of seconds with extrapolation for accurate calculation of manifold roots
%J Matematičeskoe modelirovanie
%D 2011
%P 33-58
%V 23
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_6_a2/
%G ru
%F MM_2011_23_6_a2
N. N. Kalitkin; L. V. Kuzmina. The method of seconds with extrapolation for accurate calculation of manifold roots. Matematičeskoe modelirovanie, Tome 23 (2011) no. 6, pp. 33-58. http://geodesic.mathdoc.fr/item/MM_2011_23_6_a2/

[1] Korn G., Korn T., Spravochnik po matematike; dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1968, 720 pp. | MR

[2] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. N., Chislennye metody, 3-e izdanie, Binom, Laboratoriya znanii, M., 2004, 636 pp.

[3] Voevodin V. V., Chislennye metody algebry; teoriya i algorifmy, Nauka, M., 1966 | MR | Zbl

[4] Uilkinson Dzh. Ch., Algebraicheskaya problema sobstvennykh znachenii, Nauka, M., 1970

[5] Kalitkin N. N., Chislennye metody, Nauka, M., 1978, 512 pp. | MR

[6] Zeng Z., “Computing multiple roots of inexact polynomials”, Math. Comput., 74 (2005), 869–903 | MR | Zbl

[7] Kalitkin N. N., Poshivailo I. P., “Opredelenie kratnosti kornya nelineinogo algebraicheskogo uravneniya”, ZhVM i MF, 48:7 (2008), 1–6 | MR

[8] Kalitkin N. N., Poshivailo I. P., “O vychislenii prostykh i kratnykh kornei nelineinogo uravneniya”, Matematicheskoe modelirovanie, 20:7 (2008), 57–64 | MR | Zbl

[9] Kalitkin N. N., Kuzmina L. V., “Vychislenie kornei uravneniya i opredelenie ikh kratnosti”, Matematicheskoe modelirovanie, 22:7 (2010), 33–52 | MR | Zbl