The Science of Programming Matrix Computations

The Formal Linear Algebra Methods Environment (FLAME) encompasses a methodology for deriving an algorithm for a dense linear algebra operation hand-in-hand with its proof of correctness as well as an approach to represent (and code) the resulting algorithm. This books reviews the foundations of FLAME: the derivation methodology, the notation, and the high-level Application Programming Interfaces, which are applied to basic linear algebra operations as well as operations for the solution of linear systems. While the text targets the novice, its emphasis on high performance algorithms should also be of interest to the expert.