@Article{Bientinesi:2005:SDD, author = "Paolo Bientinesi and John A. Gunnels and Margaret E. Myers and Enrique S. Quintana-Ort\'{i} and Robert A. van de Geijn", title = "The Science of Deriving Dense Linear Algebra Algorithms", journal = "{ACM} Transactions on Mathematical Software", volume = "31", number = "1", month = mar, year = "2005", pages = "1--26", URL = "http://doi.acm.org/10.1145/1055531.1055532", abstract = "In this paper we present a systematic approach to the derivation of families of high-performance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is generated. The paper is structured so that it can be used as a tutorial for novices. However, the method has been shown to yield new, high-performance algorithms for well-studied linear algebra operations and should also be of interest to those who wish to produce best-in-class high-performance codes. ", }