Algorithm 979: Recursive Algorithms for Dense Linear Algebra-The ReLAPACK Collection

摘要

To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries, such as linear algebra package (LAPACK), commonly implement operations as blocked algorithms. However, to achieve near-optimal performance with such algorithms, significant tuning is required. In contrast, recursive algorithms are virtually tuning free and attain similar performance. In this article, we first analyze and compare blocked and recursive algorithms in terms of performance and then introduce recursive LAPACK (ReLAPACK), an open-source library of recursive algorithms to seamlessly replace many of LAPACK's blocked algorithms. In most scenarios, ReLAPACK outperforms reference LAPACK and in many situations improves upon the performance of optimized libraries.