Topical Issue Applied and Numerical Linear Algebra (2/2)

Abstract

The present special issue of the GAMM Mitteilungen, which is the second of a two-part series, contains contributions on the topic of Applied and Numerical Linear Algebra, compiled by the GAMM Activity Group of the same name. The Activity Group has already contributed special issues to the GAMM Mitteilungen in 2004, 2006, and 2013. Because of the rapid development both in the theoretical foundations and the applicability of numerical linear algebra techniques throughout science and engineering, it is time again to survey the field and present the results to the readers of the GAMM Mitteilungen. We are happy that eight authors or teams of authors have accepted our invitation to report on recent research highlights in Applied Numerical Linear Algebra, and to point out the relevant literature as well as software. This work by Federico Poloni reviews a family of algorithms for Lyapunov- and Riccati-type equations which are all related by the idea of doubling. The algorithms are compared and their connections are highlighted. The paper also discusses open problems relating to their theory.