The paper considers applications of the linearization method to computing points of the finite regular and singular spectra of two-parameter polynomial matrices, of pencils of polynomial matrices of general form, and of two-parameter pencils of constant and polynomial matrices.
This method allows one to reduce the solution of the spectral problems mentioned above to the solution of the generalized eigenproblem for regular matrix pencils, which is a classical problem of algebra. Also the linearization method is applied to computing the zeros of a polynomial in two variables and the common zeros of a sequence of polynomials in two variables. Bibliography: 3 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Kublanovskaya and V. B. Khazanov, “To solving problems of algebra for two-parameter matrices. 3,” Zap. Nauch. Semin. POMI, 359, 165–207 (2008).
V. N. Kublanovskaya and V. B. Khazanov, Numerical Methods for Solving Parametric Problems of Algebra. Part 1. One-Parameter Problems [in Russian], Nauka, St. Petersburg (2004).
V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matrices. 1,” Zap. Nauch. Semin. POMI, 359, 107–149 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 367, 2009, pp. 121–144.
Rights and permissions
About this article
Cite this article
Kublanovskaya, V.N. To solving problems of algebra for two-parameter matrices. IV. J Math Sci 165, 562–573 (2010). https://doi.org/10.1007/s10958-010-9826-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-9826-z