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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2007 Volume 346, Pages 131–148 (Mi znsl92)

This article is cited in 1 paper

To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix

V. N. Kublanovskaya

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: For a general multiparameter polynomial matrix $F(\overline{\lambda})$, solution of the equation $F(\overline{\lambda})x=0$ at points of the finite spectrum of $F(\overline{\lambda})$ is considered. Points of the spectrum of $F(\overline{\lambda})$ are classified in terms of solutions of the determinantal system of nonlinear algebraic equations and also in terms of zeros of certain scalar polynomials (in particular, the characteristic polynomial of the matrix).
Algorithms for computing points of the finite regular spectrum of the matrix with the corresponding vectors are presented.

UDC: 519

Received: 07.05.2007


 English version:
Journal of Mathematical Sciences (New York), 2008, 150:2, 1989–1997

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