Geodesic
Multidimensional parametrization and numerical solution of systems of nonlinear equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 255-267

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

The numerical solution of a system of nonlinear algebraic or transcendental equations is examined within the framework of the parameter continuation method. An earlier result of the author according to which the best parameters should be sought in the tangent space of the solution set of this system is now refined to show that the directions of the eigenvectors of a certain linear self-adjoint operator should be used for finding these parameters. These directions correspond to the extremal values of the quadratic form associated with the above operator. The parametric approximation of curves and surfaces is considered. 
@article{ZVMMF_2010_50_2_a5,
     author = {E. B. Kuznetsov},
     title = {Multidimensional parametrization and numerical solution of systems of nonlinear equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {255--267},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a5/}
}
TY  - JOUR
AU  - E. B. Kuznetsov
TI  - Multidimensional parametrization and numerical solution of systems of nonlinear equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 255
EP  - 267
VL  - 50
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a5/
LA  - ru
ID  - ZVMMF_2010_50_2_a5
ER  - 
%0 Journal Article
%A E. B. Kuznetsov
%T Multidimensional parametrization and numerical solution of systems of nonlinear equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 255-267
%V 50
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a5/
%G ru
%F ZVMMF_2010_50_2_a5
E. B. Kuznetsov. Multidimensional parametrization and numerical solution of systems of nonlinear equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 255-267. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a5/