%0 Journal Article
%J Parallel Computing
%D 2018
%T Incomplete Sparse Approximate Inverses for Parallel Preconditioning
%A Hartwig Anzt
%A Thomas Huckle
%A Jürgen Bräckle
%A Jack Dongarra
%X In this paper, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. In a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.
%B Parallel Computing
%V 71
%P 1–22
%8 2018-01
%G eng
%U http://www.sciencedirect.com/science/article/pii/S016781911730176X
%! Parallel Computing
%R 10.1016/j.parco.2017.10.003
%0 Conference Proceedings
%B Proceedings of the 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
%D 2016
%T Batched Generation of Incomplete Sparse Approximate Inverses on GPUs
%A Hartwig Anzt
%A Edmond Chow
%A Thomas Huckle
%A Jack Dongarra
%X Incomplete Sparse Approximate Inverses (ISAI) have recently been shown to be an attractive alternative to exact sparse triangular solves in the context of incomplete factorization preconditioning. In this paper we propose a batched GPU-kernel for the efficient generation of ISAI matrices. Utilizing only thread-local memory allows for computing the ISAI matrix with very small memory footprint. We demonstrate that this strategy is faster than the existing strategy for generating ISAI matrices, and use a large number of test matrices to assess the algorithm's efficiency in an iterative solver setting.
%B Proceedings of the 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
%S ScalA '16
%P 49–56
%8 2016-11
%@ 978-1-5090-5222-6
%G eng
%R 10.1109/ScalA.2016.11