Solution of systems of nonlinear algebraic equations in three variables. Methods and algorithms. 3

An approach to constructing methods for solving systems of nonlinear algebraic equations in three variables (SNAEs-3) is suggested. This approach is based on the interrelationship between solutions of SNAEs-3, and solutions of spectral problems for two- and three-parameter polynomial matrices and for pencils of two-parameter matrices. Methods for computing all of the finite zero-dimensional roots of a SNAE-3 requiring no initial approximations of them are suggested. Some information on $k$-dimensional $(k>0)$ roots of SNAEs-3 useful for a further analysis of them is obtained. Bibliography: 17 titles.