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A deflation method for regular matrix pencils

Pereira, E. ; Rosa, Cecília

Applied Mathematics and Computation Vol. 218, Nº 6, pp. 2913 - 2920, November, 2011.

ISSN (print): 1873-5649
ISSN (online): 0096-3003

Scimago Journal Ranking: 1,05 (in 2011)

Digital Object Identifier: 10.1016/j.amc.2011.08.034

A generalization of the concept of eigenvalue is introduced for a matrix pencil and it is called eigenpencil; an eigenpencil is a pencil itself and it contains part of the spectral information of the matrix pencil. A Wielandt type deflation procedure for regular matrix pencils is developed, using eigenpencils and supposing that they can have both finite and infinite eigenvalues. A numerical example illustrates the proposed method.