Optimal Parallel Solution of Sparse Triangular Systems

Optimal Parallel Solution of Sparse Triangular Systems

This paper describes a method for the parallel solution of tr/ans_lar sets of equations, appropriate when there are many rlght-hand sides. By preproceuing, the method can reduce the number of parsl/el steps required to solve Zz = b compared to parallel forward or backsolve. AppUcations are to iterative solvers with tzian_d&r preconditioners, to structural sns]ysds, or to power system= applicati...

Highly Parallel Sparse Triangular Solution

Structure-adaptive parallel solution of sparse triangular linear systems

Solving sparse triangular systems of linear equations is a performance bottleneck in many methods for solving more general sparse systems. Both for direct methods and for many iterative preconditioners, it is used to solve the system or improve an approximate solution, often across many iterations. Solving triangular systems is notoriously resistant to parallelism, however, and existing paralle...

On Parallel Solution of Sparse Triangular Linear Systems in CUDA

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many sparse matrix computational kernels such as sparse matrix-vector products and sparse matrix-matrix products. Solving linear systems with sparse triangular struc...

A Fast Reordering Algorithm for Parallel Sparse Triangular Solution

A space-efficient partitioned representation of the inverse of a unit lower triangular matrix L may be used for efficiently solving sparse triangular systems on massively parallel computers. The number of steps required in the parallel triangular solution is equal to the number of subsets of elementary triangular matrices in the partitioned representation of the inverse. Alvarado and Schreiber ...