Abstract: | New methods of solving nonlinear algebraic systems in two variables are suggested, which make it possible to find all zero-dimensional
roots without knowing initial approximations. The first method reduces the solution of nonlinear algebraic systems to eigenvalue
problems for a polynomial matrix pencil. The second method is based on the rank factorization of a two-parameter polynomial
matrix, allowing, us to compute the GCD of a set of polynomials and all zero-dimensional roots of the GCD. Bibliography: 10
titles.
Translated by V. N. Kublanovskaya
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 71–96 |