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Schur complement of general H ‐matrices
Author(s) -
Bru R.,
Corral C.,
Giménez I.,
Mas J.
Publication year - 2009
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.668
Subject(s) - schur complement , schur's theorem , mathematics , schur product theorem , complement (music) , schur's lemma , schur decomposition , invertible matrix , schur algebra , matrix (chemical analysis) , class (philosophy) , pure mathematics , combinatorics , algebra over a field , eigenvalues and eigenvectors , computer science , physics , chemistry , classical orthogonal polynomials , biochemistry , gegenbauer polynomials , chromatography , quantum mechanics , artificial intelligence , complementation , orthogonal polynomials , gene , phenotype
It is well known that the Schur complement of some H ‐matrices is an H ‐matrix. In this paper, the Schur complement of any general H ‐matrix is studied. In particular, it is proved that the Schur complement, if it exists, is an H ‐matrix and the class to which the Schur complement belongs is studied. In addition, results are given for singular irreducible H ‐matrices and for the Schur complement of nonsingular irreducible H ‐matrices. Copyright © 2009 John Wiley & Sons, Ltd.