Structure-adaptive parallel solution of sparse triangular linear systems

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...

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...

Structure-Aware Parallel Algorithm for Solution of Sparse Triangular Linear Systems

Used in solution of linear systems, least squares Many times iteratively Both direct and iterative methods Example: Preconditioned Conjugate Gradient (PCG) With Incomplete-Cholesky as preconditioner Same number of non-zeros as coe cient matrix or more Usually, half of iteration’s operations is triangular solve -If triangular solve doesn’t scale: Parallel PCG’s speedup is at most (2) According t...

Highly Parallel Sparse Triangular Solution