Rapid Development of High-Performance Linear Algebra Libraries

Abstract. We present a systematic methodology for deriving and implementing linear algebra libraries. It is quite common that an application requires a library of routines for the computation of linear algebra operations that are not (exactly) supported by commonly used libraries like LAPACK. In this situation, the appli-cation developer has the option of casting the operation into one supported by an existing library, often at the expense of performance, or implementing a custom library, often requiring considerable effort. Our recent discovery of a methodol-ogy based on formal derivation of algorithm allows such a user to quickly de-rive proven correct algorithms. Furthermore it provides an API that allows the so-derived algorithms to be quickly translated into high-performance implemen-tations.