Geodesic
Connection between the spectral problem for linear matrix pencils and some problems of algebra
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 98-116

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

We suggest a method by which the solution of systems of nonlinear algebraic equations in one and two variables can be reduced to the spectral problem for linear pencils of two matrices and for a system of two matrix pencils of two matrices, respectively. This method is substantially different from the traditional methods of solution; at the same time it is useful for the study of the solvability and the determination of the number of solutions of such systems. We propose a modification of the well-known elimination method for the solution of nonlinear algebraic systems of two equations in two unknowns which provides a new approach to studying and solving the problem. 
@article{ZNSL_1978_80_a5,
     author = {V. N. Kublanovskaya},
     title = {Connection between the spectral problem for linear matrix pencils and some problems of algebra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--116},
     publisher = {mathdoc},
     volume = {80},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a5/}
}
TY  - JOUR
AU  - V. N. Kublanovskaya
TI  - Connection between the spectral problem for linear matrix pencils and some problems of algebra
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1978
SP  - 98
EP  - 116
VL  - 80
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a5/
LA  - ru
ID  - ZNSL_1978_80_a5
ER  - 
%0 Journal Article
%A V. N. Kublanovskaya
%T Connection between the spectral problem for linear matrix pencils and some problems of algebra
%J Zapiski Nauchnykh Seminarov POMI
%D 1978
%P 98-116
%V 80
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a5/
%G ru
%F ZNSL_1978_80_a5
V. N. Kublanovskaya. Connection between the spectral problem for linear matrix pencils and some problems of algebra. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 98-116. http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a5/