Sparse matrix factorization involves a mix of regular and irregular computation, which is a particular challenge when trying to obtain high-performance on the highly parallel general-purpose computing cores available on graphics processing units (GPUs). We present a sparse multifrontal QR factorization method that meets this challenge, and is up to ten times faster than a highly optimized method on a multicore CPU. Our method is unique compared with prior methods, since it factorizes many frontal matrices in parallel, and keeps all the data transmitted between frontal matrices on the GPU. A novel bucket scheduler algorithm extends the communication-avoiding QR factorization for dense matrices, by exploiting more parallelism and by exploiting the staircase form present in the frontal matrices of a sparse multifrontal method.
This is joint work with Nuri Yeralan and Sanjay Ranka.