A resultant approach to computing vector characteristics of multiparameter polynomial matrices

V. B. Khazanov

Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 182-214

Résumé

Known types of resultant matrices corresponding to one-parameter matrix polynomials are generalized to the multiparameter case. Based on the resultant approach suggested, methods for solving the following problems for multiparameter polynomial matrices are developed: computing a basis of the matrix range, computing a minimal basis of the right null-space, and constructing Jordan chains and semilattices of vectors associated with a multiple spectrum point. In solving these problems, the original polynomial matrix is not transformed. Methods for solving other parameter problems of algebra can be developed on the basis of the method for computing a minimal basis of the null-space of a polynomial matrix. Issues concerning the optimality of computing the null-spaces of sparse resultant matrices and numerical precision are not considered.