A Fast Dense Triangular Solve in CUDA

Abstract

The level 2 BLAS operation _trsv performs a dense triangular solve and is often used in the solve phase of a direct solver following a matrix factorization. With the advent of manycore architectures reducing the cost of compute-bound parts of the computation, memory-bound operations such as this kernel become increasingly important. This is particularly noticeable in sparse direct solvers used for optimization applications where multiple memory-bound solves follow each (traditionally expensive) compute-bound factorization. In this paper, a high performance implementation of the triangular solve is developed through an analysis of theoretical and practical bounds on its run time. This implementation outperforms the CUBLAS by a factor of 5--15.