Badía, José M.; Benner, Peter; Castillo, Maribel; Faßbender, Heike; Mayo, Rafael; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio Strategies for parallelizing the solution of rational matrix equations. (English) Zbl 1158.65317 Bischof, Christian (ed.) et al., Parallel computing: Architectures, algorithms and applications. Selected papers based on the presentations at the international parallel computing conference (ParCo 2007), Aachen, Germany, September 4–7, 2007. Amsterdam: IOS Press (ISBN 978-1-58603-796-3/hbk). Advances in Parallel Computing 15, 255-262 (2008). Summary: We apply different strategies to parallelize a structure-preserving doubling method for the rational matrix equation \(X = Q + LX^{-1} L^T\). Several levels of parallelism are exploited to enhance performance, and standard sequential and parallel linear algebra libraries are used to obtain portable and efficient implementations of the algorithms. Experimental results on a shared-memory multiprocessor show that a coarse-grain approach which combines two MPI processes with a multithreaded implementation of BLAS in general yields the highest performance.For the entire collection see [Zbl 1149.68004]. Cited in 1 Document MSC: 65F30 Other matrix algorithms (MSC2010) 65Y05 Parallel numerical computation 15A24 Matrix equations and identities Keywords:parallel computation; numerical examples; rational matrix equation; algorithms Software:BLAS PDFBibTeX XMLCite \textit{J. M. Badía} et al., Adv. Parallel Comput. 15, 255--262 (2008; Zbl 1158.65317)