Response to Comment on 'Preconditioning of matrices partitioned in 2 × 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM'. Issue 3 (28th February 2012)

• Record Type: Journal Article
• Authors: Axelsson, Owe; Blaheta, Radim
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 3(2013:May)
• Page Start: 536
• Page End: 539
• Publication Date: 2012-02-28
• Subjects: Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.816
• Languages: English
• ISSNs: 1070-5325

Abstract

<abstract abstract-type="main" id="nla816-abs-0001"> <title>SUMMARY</title> <p id="nla816-para-0001">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.</p> <p id="nla816-para-0002">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'.</p> <p id="nla816-para-0003">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 &amp; Sons, Ltd.</p> </abstract>