Assessing Sparse Triangular Linear System Solvers on GPUs

Abstract

An important number of Numerical Linear Algebra methods to tackle problems in diverse fields of science and engineering, rely heavily on the solution of one or many sparse triangular linear systems. Since the early years, this has motivated numerous efforts that seek to produce efficientimplementations of this kernel for most hardware platforms. However, this operation implies strong data dependencies and unbalanced computations that difficult the concurrency, specially when massively-parallel processors such as GPUs are employed. In this work we review the different techniques to expose the data parallelism in this operation with specialattention to the many-core based proposals. Additionally, we experimentally evaluate the two most successful approaches, namely the routine that is included in CUSPARSE library and the synchronization free method of W. Liu et al. [1]. Finally, we advance in the characterization of the triangular sparse linear systems to select the best solver in each case.