Fine-Grained Multithreading for the Multifrontal $QR$ Factorization of Sparse Matrices

The advent of multicore processors represents a disruptive event in the history of computer science as conventional parallel programming paradigms are proving incapable of fully exploiting their potential for concurrent computations. The need for different or new programming models clearly arises from recent studies which identify fine-granularity and dynamic execution as the keys to achieving high efficiency on multicore systems. This work presents an approach to the parallelization of the multifrontal method for the $QR$ factorization of sparse matrices specifically designed for multicore based systems. High efficiency is achieved through a fine-grained partitioning of data and a dynamic scheduling of computational tasks relying on a dataflow parallel programming model. Experimental results show that an implementation of the proposed approach achieves higher performance and better scalability than existing equivalent software