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The resultant approach to computing vector characteristics of multiparameter polynomial matrices

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Abstract

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 the 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 parametric 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. Bibliography: 19 titles.

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Authors and Affiliations

  1. St.Petersburg State Marine Technical University, St.Petersburg, Russia

    V. B. Khazanov

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  1. V. B. Khazanov
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__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 182–214.

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Khazanov, V.B. The resultant approach to computing vector characteristics of multiparameter polynomial matrices. J Math Sci 137, 4862–4878 (2006). https://doi.org/10.1007/s10958-006-0284-6

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  • DOI: https://doi.org/10.1007/s10958-006-0284-6

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