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Response to Comment on ‘Preconditioning of matrices partitioned in 2 × 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM’
Author(s) -
Axelsson Owe,
Blaheta Radim
Publication year - 2013
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.816
Subject(s) - corollary , proposition , mathematics , saddle , eigenvalues and eigenvectors , block (permutation group theory) , saddle point , finite element method , mathematical economics , algebra over a field , combinatorics , pure mathematics , mathematical optimization , engineering , philosophy , epistemology , geometry , physics , quantum mechanics , structural engineering
SUMMARY As has been pointed out in a study by Cao, there is an erroneous omission in the study by Axelsson, Corollary 3.2 and Proposition 3.2, and the authors thank Zhi‐hao Cao for pointing this out. We mention, however, that these are side results and do not influence the major result of the paper ‘Preconditioning of matrices partitioned in 2 by 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM’. In this reply, we give a short background to the relations between inverses of saddle point matrices, thereby providing justified references to previous publications of the topic and present a corrected and extended version of Proposition 3.2. This gives an alternative presentation of the statements in the study by Cao, which might be useful for readers. Copyright © 2012 John Wiley & Sons, Ltd.