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An approach to solving multiparameter algebraic problems

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Abstract

An approach to solving the following multiparameter algebraic problems is suggested: (1) spectral problems for singular matrices polynomially dependent on q≥2 spectral parameters, namely: the separation of the regular and singular parts of the spectrum, the computation of the discrete spectrum, and the construction of a basis that is free of a finite regular spectrum of the null-space of polynomial solutions of a multiparameter polynomial matrix; (2) the execution of certain operations over scalar and matrix multiparameter polynomials, including the computation of the GCD of a sequence of polynomials, the division of polynomials by their common divisor, and the computation of relative factorizations of polynomials; (3) the solution of systems of linear algebraic equations with multiparameter polynomial matrices and the construction of inverse and pseudoinverse matrices. This approach is based on the so-called ΔW-q factorizations of polynomial q-parameter matrices and extends the method for solving problems for one- and two-parameter polynomial matrices considered in [1–3] to an arbitrary q≥2. Bibliography: 12 titles.

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Authors
  1. V. N. Kublanovskaya
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 191–246.

Translated by V. N. Kublanovskaya.

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Kublanovskaya, V.N. An approach to solving multiparameter algebraic problems. J Math Sci 89, 1715–1749 (1998). https://doi.org/10.1007/BF02355374

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  • DOI: https://doi.org/10.1007/BF02355374

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