Scaling Dense Linear Algebra on Multicore and Beyond: a Survey

The present trend in big-data analytics is to exploit algorithms with (sub-)linear time complexity, in this sense it is usually worth to investigate if the available techniques can be approximated to reach an affordable complexity. However, there are still problems in data science and engineering that involve algorithms with higher time complexity, like matrix inversion or Singular Value Decomposition (SVD). This work presents the results of a survey that reviews a number of tools meant to perform dense linear algebra at ``Big Data'' scale: namely, the proposed approach aims first to define a feasibility boundary for the problem size of shared-memory matrix factorizations, then to understand whether it is convenient to employ specific tools meant to scale out such dense linear algebra tasks on distributed platforms. The survey will eventually discuss the presented tools from the point of view of domain experts (data scientist, engineers), hence focusing on the trade-off between usability and performance.