Methods for solving spectral problems for multiparameter matrix pencils. (English. Russian original) Zbl 1073.65523

Khazanov, V. B.

J. Math. Sci., New York 127, No. 3, 2033-2050 (2005); translation from Zap. Nauchn. Semin. POMI 296, 139-168 (2003).

Summary: Methods for solving the partial eigenproblem for multiparameter regular pencils of real matrices, which allow one to improve given approximations of an eigenvector and the associated point of the spectrum (both finite and infinite) are suggested. Ways of extending the methods to complex matrices, polynomial matrices, and coupled multiparameter problems are indicated.

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
15A22	Matrix pencils
15A18	Eigenvalues, singular values, and eigenvectors
15A54	Matrices over function rings in one or more variables

Keywords:

Newton method; partial eigenproblem; multiparameter regular pencils; eigenvector; complex matrices; polynomial matrices

References:

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