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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
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:  
 
Secondary Classification:  
 
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 Lshaped 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:  