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Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE 016 721 340

Author(s):

Pereira, E.; Vitoria, J.:

Shorttitle:

Block eigenvalues of partitioned matrices, with an application to matrix polynomials

Source:

Comput. Math. Appl. 42, No. 8 - 9, 1177 - 1188 (2001).

Classification:

Primary Classification:

65F15

Eigenvalues, eigenvectors

Secondary Classification:

15A33

Matrices over special rings quaternions, finite fields, etc.

47A56

Functions whose values are linear operators operator and matrix valued functions, etc., including analytic and meromorphic ones

Keywords:

matrix polynomials; matrix roots; numerical factorization; block deflation method; polynomials with commuting matrix coefficients;

Review:

The most immediate generalization of complex polynomials are
matrix polynomials where the coefficients and the variable are
commuting matrices over C. In the paper the numerical method of
solving the related generalized polynomial algebraic equation is
presented. It uses, basically, a block version of Wieland
deflation procedure, applied to the the block companion matrix of
the generalized polynomial in question. The procedure preserves a
certain L-shaped structure of the sequence of deflated matrices.
In essence, this algorithm extends the Dennis, Traub and Weber
computation of a matrix root (called ``solvent") by providing all
of them.

Remarks to the editors:

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