Response to Comment on Preconditioning of matrices partitioned in 2 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM

0397045 - ÚGN 2014 RIV GB eng J - Článek v odborném periodiku
Axelsson, Owe - Blaheta, Radim
Response to Comment on Preconditioning of matrices partitioned in 2 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM.
Numerical Linear Algebra with Applications. Roč. 20, č. 3 (2013), s. 536-539. ISSN 1070-5325. E-ISSN 1099-1506
Institucionální podpora: RVO:68145535
Klíčová slova: saddle point matrices * inverses * preconditioning
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.424, rok: 2013
http://onlinelibrary.wiley.com/doi/10.1002/nla.816/pdf

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.
Trvalý link: http://hdl.handle.net/11104/0224730